A Survey on Multi-Task Learning
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paper_title: A Survey on Transfer Learning

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A major assumption in many machine learning and data mining algorithms is that the training and future data must be in the same feature space and have the same distribution. However, in many real-world applications, this assumption may not hold. For example, we sometimes have a classification task in one domain of interest, but we only have sufficient training data in another domain of interest, where the latter data may be in a different feature space or follow a different data distribution. In such cases, knowledge transfer, if done successfully, would greatly improve the performance of learning by avoiding much expensive data-labeling efforts. In recent years, transfer learning has emerged as a new learning framework to address this problem. This survey focuses on categorizing and reviewing the current progress on transfer learning for classification, regression, and clustering problems. In this survey, we discuss the relationship between transfer learning and other related machine learning techniques such as domain adaptation, multitask learning and sample selection bias, as well as covariate shift. We also explore some potential future issues in transfer learning research.
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paper_title: A Convex Formulation for Learning Task Relationships in Multi-Task Learning

paper_content:

Multi-task learning is a learning paradigm which seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this paper, we propose a regularization formulation for learning the relationships between tasks in multi-task learning. This formulation can be viewed as a novel generalization of the regularization framework for single-task learning. Besides modeling positive task correlation, our method, called multi-task relationship learning (MTRL), can also describe negative task correlation and identify outlier tasks based on the same underlying principle. Under this regularization framework, the objective function of MTRL is convex. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multi-task learning setting and then generalize it to the asymmetric setting as well. We also study the relationships between MTRL and some existing multi-task learning methods. Experiments conducted on a toy problem as well as several benchmark data sets demonstrate the effectiveness of MTRL.
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paper_title: A Regularization Approach to Learning Task Relationships in Multitask Learning

paper_content:

Multitask learning is a learning paradigm that seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this article, we propose a regularization approach to learning the relationships between tasks in multitask learning. This approach can be viewed as a novel generalization of the regularized formulation for single-task learning. Besides modeling positive task correlation, our approach—multitask relationship learning (MTRL)—can also describe negative task correlation and identify outlier tasks based on the same underlying principle. By utilizing a matrix-variate normal distribution as a prior on the model parameters of all tasks, our MTRL method has a jointly convex objective function. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multitask learning setting and then generalize it to the asymmetric setting as well. We also discuss some variants of the regularization approach to demonstrate the use of other matrix-variate priors for learning task relationships. Moreover, to gain more insight into our model, we also study the relationships between MTRL and some existing multitask learning methods. Experiments conducted on a toy problem as well as several benchmark datasets demonstrate the effectiveness of MTRL as well as its high interpretability revealed by the task covariance matrix.
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paper_title: Multitask Learning

paper_content:

Multitask Learning is an approach to inductive transfer that improves generalization by using the domain information contained in the training signals of related tasks as an inductive bias. It does this by learning tasks in parallel while using a shared representation; what is learned for each task can help other tasks be learned better. This paper reviews prior work on MTL, presents new evidence that MTL in backprop nets discovers task relatedness without the need of supervisory signals, and presents new results for MTL with k-nearest neighbor and kernel regression. In this paper we demonstrate multitask learning in three domains. We explain how multitask learning works, and show that there are many opportunities for multitask learning in real domains. We present an algorithm and results for multitask learning with case-based methods like k-nearest neighbor and kernel regression, and sketch an algorithm for multitask learning in decision trees. Because multitask learning works, can be applied to many different kinds of domains, and can be used with different learning algorithms, we conjecture there will be many opportunities for its use on real-world problems.
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paper_title: Multi-task learning for classification with dirichlet process priors

paper_content:

Consider the problem of learning logistic-regression models for multiple classification tasks, where the training data set for each task is not drawn from the same statistical distribution. In such a multi-task learning (MTL) scenario, it is necessary to identify groups of similar tasks that should be learned jointly. Relying on a Dirichlet process (DP) based statistical model to learn the extent of similarity between classification tasks, we develop computationally efficient algorithms for two different forms of the MTL problem. First, we consider a symmetric multi-task learning (SMTL) situation in which classifiers for multiple tasks are learned jointly using a variational Bayesian (VB) algorithm. Second, we consider an asymmetric multi-task learning (AMTL) formulation in which the posterior density function from the SMTL model parameters (from previous tasks) is used as a prior for a new task: this approach has the significant advantage of not requiring storage and use of all previous data from prior tasks. The AMTL formulation is solved with a simple Markov Chain Monte Carlo (MCMC) construction. Experimental results on two real life MTL problems indicate that the proposed algorithms: (a) automatically identify subgroups of related tasks whose training data appear to be drawn from similar distributions; and (b) are more accurate than simpler approaches such as single-task learning, pooling of data across all tasks, and simplified approximations to DP.
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paper_title: Multi-task learning for HIV therapy screening

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We address the problem of learning classifiers for a large number of tasks. We derive a solution that produces resampling weights which match the pool of all examples to the target distribution of any given task. Our work is motivated by the problem of predicting the outcome of a therapy attempt for a patient who carries an HIV virus with a set of observed genetic properties. Such predictions need to be made for hundreds of possible combinations of drugs, some of which use similar biochemical mechanisms. Multi-task learning enables us to make predictions even for drug combinations with few or no training examples and substantially improves the overall prediction accuracy.
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paper_title: Heterogeneous multitask learning with joint sparsity constraints

paper_content:

Multitask learning addresses the problem of learning related tasks that presumably share some commonalities on their input-output mapping functions. Previous approaches to multitask learning usually deal with homogeneous tasks, such as purely regression tasks, or entirely classification tasks. In this paper, we consider the problem of learning multiple related tasks of predicting both continuous and discrete outputs from a common set of input variables that lie in a high-dimensional feature space. All of the tasks are related in the sense that they share the same set of relevant input variables, but the amount of influence of each input on different outputs may vary. We formulate this problem as a combination of linear regressions and logistic regressions, and model the joint sparsity as L1/L∞ or L1/L2 norm of the model parameters. Among several possible applications, our approach addresses an important open problem in genetic association mapping, where the goal is to discover genetic markers that influence multiple correlated traits jointly. In our experiments, we demonstrate our method in this setting, using simulated and clinical asthma datasets, and we show that our method can effectively recover the relevant inputs with respect to all of the tasks.
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paper_title: Convex multi-task feature learning

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We present a method for learning sparse representations shared across multiple tasks. This method is a generalization of the well-known single-task 1-norm regularization. It is based on a novel non-convex regularizer which controls the number of learned features common across the tasks. We prove that the method is equivalent to solving a convex optimization problem for which there is an iterative algorithm which converges to an optimal solution. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the former step it learns task-specific functions and in the latter step it learns common-across-tasks sparse representations for these functions. We also provide an extension of the algorithm which learns sparse nonlinear representations using kernels. We report experiments on simulated and real data sets which demonstrate that the proposed method can both improve the performance relative to learning each task independently and lead to a few learned features common across related tasks. Our algorithm can also be used, as a special case, to simply select--not learn--a few common variables across the tasks.
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paper_title: Radial Basis Function Network for Multi-task Learning

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We extend radial basis function (RBF) networks to the scenario in which multiple correlated tasks are learned simultaneously, and present the corresponding learning algorithms. We develop the algorithms for learning the network structure, in either a supervised or unsupervised manner. Training data may also be actively selected to improve the network's generalization to test data. Experimental results based on real data demonstrate the advantage of the proposed algorithms and support our conclusions.
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paper_title: Infinite Latent SVM for Classification and Multi-task Learning

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Unlike existing nonparametric Bayesian models, which rely solely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations, we study nonparametric Bayesian inference with regularization on the desired posterior distributions. While priors can indirectly affect posterior distributions through Bayes' theorem, imposing posterior regularization is arguably more direct and in some cases can be much easier. We particularly focus on developing infinite latent support vector machines (iLSVM) and multi-task infinite latent support vector machines (MT-iLSVM), which explore the large-margin idea in combination with a nonparametric Bayesian model for discovering predictive latent features for classification and multi-task learning, respectively. We present efficient inference methods and report empirical studies on several benchmark datasets. Our results appear to demonstrate the merits inherited from both large-margin learning and Bayesian nonparametrics.
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paper_title: Multitask Learning

paper_content:

Multitask Learning is an approach to inductive transfer that improves generalization by using the domain information contained in the training signals of related tasks as an inductive bias. It does this by learning tasks in parallel while using a shared representation; what is learned for each task can help other tasks be learned better. This paper reviews prior work on MTL, presents new evidence that MTL in backprop nets discovers task relatedness without the need of supervisory signals, and presents new results for MTL with k-nearest neighbor and kernel regression. In this paper we demonstrate multitask learning in three domains. We explain how multitask learning works, and show that there are many opportunities for multitask learning in real domains. We present an algorithm and results for multitask learning with case-based methods like k-nearest neighbor and kernel regression, and sketch an algorithm for multitask learning in decision trees. Because multitask learning works, can be applied to many different kinds of domains, and can be used with different learning algorithms, we conjecture there will be many opportunities for its use on real-world problems.
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paper_title: Spike and slab variational inference for multi-task and multiple kernel learning

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We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi-task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multi-output Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.
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paper_title: Multi-task learning for classification with dirichlet process priors

paper_content:

Consider the problem of learning logistic-regression models for multiple classification tasks, where the training data set for each task is not drawn from the same statistical distribution. In such a multi-task learning (MTL) scenario, it is necessary to identify groups of similar tasks that should be learned jointly. Relying on a Dirichlet process (DP) based statistical model to learn the extent of similarity between classification tasks, we develop computationally efficient algorithms for two different forms of the MTL problem. First, we consider a symmetric multi-task learning (SMTL) situation in which classifiers for multiple tasks are learned jointly using a variational Bayesian (VB) algorithm. Second, we consider an asymmetric multi-task learning (AMTL) formulation in which the posterior density function from the SMTL model parameters (from previous tasks) is used as a prior for a new task: this approach has the significant advantage of not requiring storage and use of all previous data from prior tasks. The AMTL formulation is solved with a simple Markov Chain Monte Carlo (MCMC) construction. Experimental results on two real life MTL problems indicate that the proposed algorithms: (a) automatically identify subgroups of related tasks whose training data appear to be drawn from similar distributions; and (b) are more accurate than simpler approaches such as single-task learning, pooling of data across all tasks, and simplified approximations to DP.
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paper_title: Sparse coding for multitask and transfer learning

paper_content:

We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear combinations of the atoms of a dictionary on a high or infinite dimensional space. This assumption, together with the large quantity of available data in the multitask and transfer learning settings, allows a principled choice of the dictionary. We provide bounds on the generalization error of this approach, for both settings. Numerical experiments on one synthetic and two real datasets show the advantage of our method over single task learning, a previous method based on orthogonal and dense representation of the tasks and a related method learning task grouping.
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paper_title: Handling sparsity via the horseshoe

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This paper presents a general, fully Bayesian framework for sparse supervised-learning problems based on the horseshoe prior. The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used approaches for sparse Bayesian learning, including, among others, Laplacian priors (e.g. the LASSO) and Student-t priors (e.g. the relevance vector machine). The advantages of the horseshoe are its robustness at handling unknown sparsity and large outlying signals. These properties are justied theoretically via a representation theorem and accompanied by comprehensive empirical experiments that compare its performance to benchmark alternatives.
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paper_title: Learning Feature Selection Dependencies in Multi-task Learning

paper_content:

A probabilistic model based on the horseshoe prior is proposed for learning dependencies in the process of identifying relevant features for prediction. Exact inference is intractable in this model. However, expectation propagation offers an approximate alternative. Because the process of estimating feature selection dependencies may suffer from over-fitting in the model proposed, additional data from a multi-task learning scenario are considered for induction. The same model can be used in this setting with few modifications. Furthermore, the assumptions made are less restrictive than in other multi-task methods: The different tasks must share feature selection dependencies, but can have different relevant features and model coefficients. Experiments with real and synthetic data show that this model performs better than other multi-task alternatives from the literature. The experiments also show that the model is able to induce suitable feature selection dependencies for the problems considered, only from the training data.
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paper_title: Encoding tree sparsity in multi-task learning: a probabilistic framework

paper_content:

Multi-task learning seeks to improve the generalization performance by sharing common information among multiple related tasks. A key assumption in most MTL algorithms is that all tasks are related, which, however, may not hold in many real-world applications. Existing techniques, which attempt to address this issue, aim to identify groups of related tasks using group sparsity. In this paper, we propose a probabilistic tree sparsity (PTS) model to utilize the tree structure to obtain the sparse solution instead of the group structure. Specifically, each model coefficient in the learning model is decomposed into a product of multiple component coefficients each of which corresponds to a node in the tree. Based on the decomposition, Gaussian and Cauchy distributions are placed on the component coefficients as priors to restrict the model complexity. We devise an efficient expectation maximization algorithm to learn the model parameters. Experiments conducted on both synthetic and real-world problems show the effectiveness of our model compared with state-of-the-art baselines.
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paper_title: Exclusive Lasso for Multi-task Feature Selection

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We propose a novel group regularization which we call exclusive lasso. Unlike the group lasso regularizer that assumes covarying variables in groups, the proposed exclusive lasso regularizer models the scenario when variables in the same group compete with each other. Analysis is presented to illustrate the properties of the proposed regularizer. We present a framework of kernel based multi-task feature selection algorithm based on the proposed exclusive lasso regularizer. An efficient algorithm is derived to solve the related optimization problem. Experiments with document categorization show that our approach outperforms state-of-theart algorithms for multi-task feature selection.
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paper_title: Sparse Overlapping Sets Lasso for Multitask Learning and its Application to fMRI Analysis

paper_content:

Multitask learning can be effective when features useful in one task are also useful for other tasks, and the group lasso is a standard method for selecting a common subset of features. In this paper, we are interested in a less restrictive form of multitask learning, wherein (1) the available features can be organized into subsets according to a notion of similarity and (2) features useful in one task are similar, but not necessarily identical, to the features best suited for other tasks. The main contribution of this paper is a new procedure called Sparse Overlapping Sets (SOS) lasso, a convex optimization that automatically selects similar features for related learning tasks. Error bounds are derived for SOSlasso and its consistency is established for squared error loss. In particular, SOSlasso is motivated by multi-subject fMRI studies in which functional activity is classified using brain voxels as features. Experiments with real and synthetic data demonstrate the advantages of SOSlasso compared to the lasso and group lasso.
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paper_title: A Probabilistic Model for Dirty Multi-task Feature Selection

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Multi-task feature selection methods often make the hypothesis that learning tasks share relevant and irrelevant features. However, this hypothesis may be too restrictive in practice. For example, there may be a few tasks with specific relevant and irrelevant features (outlier tasks). Similarly, a few of the features may be relevant for only some of the tasks (outlier features). To account for this, we propose a model for multitask feature selection based on a robust prior distribution that introduces a set of binary latent variables to identify outlier tasks and outlier features. Expectation propagation can be used for efficient approximate inference under the proposed prior. Several experiments show that a model based on the new robust prior provides better predictive performance than other benchmark methods.
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paper_title: Adaptive Multi-Task Lasso: with application to eQTL detection

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To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects. However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared to the number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. ::: ::: In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively. Then we find the maximum a posteriori (MAP) estimation of regression coefficients and estimate weights of covariates jointly. This optimization procedure is efficient since it can be achieved by using a projected gradient descent and a coordinate descent procedure iteratively. Experimental results on simulated and real yeast datasets confirm that our model outperforms previous methods for finding eQTLs.
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paper_title: Tree-Guided Group Lasso for Multi-Task Regression with Structured Sparsity

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We consider the problem of learning a sparse multi-task regression, where the structure in the outputs can be represented as a tree with leaf nodes as outputs and internal nodes as clusters of the outputs at multiple granularity. Our goal is to recover the common set of relevant inputs for each output cluster. Assuming that the tree structure is available as prior knowledge, we formulate this problem as a new multi-task regularized regression called tree-guided group lasso. Our structured regularization is based on a group-lasso penalty, where groups are defined with respect to the tree structure. We describe a systematic weighting scheme for the groups in the penalty such that each output variable is penalized in a balanced manner even if the groups overlap. We present an efficient optimization method that can handle a large-scale problem. Using simulated and yeast datasets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns compared to other methods for multi-task learning.
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paper_title: Radial Basis Function Network for Multi-task Learning

paper_content:

We extend radial basis function (RBF) networks to the scenario in which multiple correlated tasks are learned simultaneously, and present the corresponding learning algorithms. We develop the algorithms for learning the network structure, in either a supervised or unsupervised manner. Training data may also be actively selected to improve the network's generalization to test data. Experimental results based on real data demonstrate the advantage of the proposed algorithms and support our conclusions.
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paper_title: Multi-level Lasso for Sparse Multi-task Regression

paper_content:

We present a flexible formulation for variable selection in multi-task regression to allow for discrepancies in the estimated sparsity patterns accross the multiple tasks, while leveraging the common structure among them. Our approach is based on an intuitive decomposition of the regression coe_cients into a product between a component that is common to all tasks and another component that captures task-specificity. This decomposition yields the Multi-level Lasso objective that can be solved efficiently via alternating optimization. The analysis of the "orthonormal design" case reveals some interesting insights on the nature of the shrinkage performed by our method, compared to that of related work. Theoretical guarantees are provided on the consistency of Multi-level Lasso. Simulations and empirical study of micro-array data further demonstrate the value of our framework.
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paper_title: Blockwise coordinate descent procedures for the multi-task lasso, with applications to neural semantic basis discovery

paper_content:

We develop a cyclical blockwise coordinate descent algorithm for the multi-task Lasso that efficiently solves problems with thousands of features and tasks. The main result shows that a closed-form Winsorization operator can be obtained for the sup-norm penalized least squares regression. This allows the algorithm to find solutions to very large-scale problems far more efficiently than existing methods. This result complements the pioneering work of Friedman, et al. (2007) for the single-task Lasso. As a case study, we use the multi-task Lasso as a variable selector to discover a semantic basis for predicting human neural activation. The learned solution outperforms the standard basis for this task on the majority of test participants, while requiring far fewer assumptions about cognitive neuroscience. We demonstrate how this learned basis can yield insights into how the brain represents the meanings of words.
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paper_title: Multi-Stage Multi-Task Feature Learning

paper_content:

Multi-task sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. Most of the existing multi-task sparse feature learning algorithms are formulated as a convex sparse regularization problem, which is usually suboptimal, due to its looseness for approximating an l0-type regularizer. In this paper, we propose a non-convex formulation for multi-task sparse feature learning based on a novel nonconvex regularizer. To solve the non-convex optimization problem, we propose a Multi-Stage Multi-Task Feature Learning (MSMTFL) algorithm; we also provide intuitive interpretations, detailed convergence and reproducibility analysis for the proposed algorithm. Moreover, we present a detailed theoretical analysis showing that MSMTFL achieves a better parameter estimation error bound than the convex formulation. Empirical studies on both synthetic and real-world data sets demonstrate the effectiveness of MSMTFL in comparison with the state of the art multi-task sparse feature learning algorithms.
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paper_title: Multitask sparsity via maximum entropy discrimination

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A multitask learning framework is developed for discriminative classification and regression where multiple large-margin linear classifiers are estimated for different prediction problems. These classifiers operate in a common input space but are coupled as they recover an unknown shared representation. A maximum entropy discrimination (MED) framework is used to derive the multitask algorithm which involves only convex optimization problems that are straightforward to implement. Three multitask scenarios are described. The first multitask method produces multiple support vector machines that learn a shared sparse feature selection over the input space. The second multitask method produces multiple support vector machines that learn a shared conic kernel combination. The third multitask method produces a pooled classifier as well as adaptively specialized individual classifiers. Furthermore, extensions to regression, graphical model structure estimation and other sparse methods are discussed. The maximum entropy optimization problems are implemented via a sequential quadratic programming method which leverages recent progress in fast SVM solvers. Fast monotonic convergence bounds are provided by bounding the MED sparsifying cost function with a quadratic function and ensuring only a constant factor runtime increase above standard independent SVM solvers. Results are shown on multitask data sets and favor multitask learning over single-task or tabula rasa methods.
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paper_title: Efficient multi-task feature learning with calibration

paper_content:

Multi-task feature learning has been proposed to improve the generalization performance by learning the shared features among multiple related tasks and it has been successfully applied to many real-world problems in machine learning, data mining, computer vision and bioinformatics. Most existing multi-task feature learning models simply assume a common noise level for all tasks, which may not be the case in real applications. Recently, a Calibrated Multivariate Regression (CMR) model has been proposed, which calibrates different tasks with respect to their noise levels and achieves superior prediction performance over the non-calibrated one. A major challenge is how to solve the CMR model efficiently as it is formulated as a composite optimization problem consisting of two non-smooth terms. In this paper, we propose a variant of the calibrated multi-task feature learning formulation by including a squared norm regularizer. We show that the dual problem of the proposed formulation is a smooth optimization problem with a piecewise sphere constraint. The simplicity of the dual problem enables us to develop fast dual optimization algorithms with low per-iteration cost. We also provide a detailed convergence analysis for the proposed dual optimization algorithm. Empirical studies demonstrate that, the dual optimization algorithm quickly converges and it is much more efficient than the primal optimization algorithm. Moreover, the calibrated multi-task feature learning algorithms with and without the squared norm regularizer achieve similar prediction performance and both outperform the non-calibrated ones. Thus, the proposed variant not only enables us to develop fast optimization algorithms, but also keeps the superior prediction performance of the calibrated multi-task feature learning over the non-calibrated one.
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paper_title: A Regularization Approach to Learning Task Relationships in Multitask Learning

paper_content:

Multitask learning is a learning paradigm that seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this article, we propose a regularization approach to learning the relationships between tasks in multitask learning. This approach can be viewed as a novel generalization of the regularized formulation for single-task learning. Besides modeling positive task correlation, our approach—multitask relationship learning (MTRL)—can also describe negative task correlation and identify outlier tasks based on the same underlying principle. By utilizing a matrix-variate normal distribution as a prior on the model parameters of all tasks, our MTRL method has a jointly convex objective function. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multitask learning setting and then generalize it to the asymmetric setting as well. We also discuss some variants of the regularization approach to demonstrate the use of other matrix-variate priors for learning task relationships. Moreover, to gain more insight into our model, we also study the relationships between MTRL and some existing multitask learning methods. Experiments conducted on a toy problem as well as several benchmark datasets demonstrate the effectiveness of MTRL as well as its high interpretability revealed by the task covariance matrix.
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paper_title: Probabilistic Multi-Task Feature Selection

paper_content:

Recently, some variants of the l1 norm, particularly matrix norms such as the l1,2 and l1,∞ norms, have been widely used in multi-task learning, compressed sensing and other related areas to enforce sparsity via joint regularization. In this paper, we unify the l1,2 and l1,∞ norms by considering a family of l1,q norms for 1 < q < ∞ and study the problem of determining the most appropriate sparsity enforcing norm to use in the context of multi-task feature selection. Using the generalized normal distribution, we provide a probabilistic interpretation of the general multi-task feature selection problem using the l1,q norm. Based on this probabilistic interpretation, we develop a probabilistic model using the noninformative Jeffreys prior. We also extend the model to learn and exploit more general types of pairwise relationships between tasks. For both versions of the model, we devise expectation-maximization (EM) algorithms to learn all model parameters, including q, automatically. Experiments have been conducted on two cancer classification applications using microarray gene expression data.
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paper_title: On Multiplicative Multitask Feature Learning

paper_content:

We investigate a general framework of multiplicative multitask feature learning which decomposes each task's model parameters into a multiplication of two components. One of the components is used across all tasks and the other component is task-specific. Several previous methods have been proposed as special cases of our framework. We study the theoretical properties of this framework when different regularization conditions are applied to the two decomposed components. We prove that this framework is mathematically equivalent to the widely used multitask feature learning methods that are based on a joint regularization of all model parameters, but with a more general form of regularizers. Further, an analytical formula is derived for the across-task component as related to the task-specific component for all these regularizers, leading to a better understanding of the shrinkage effect. Study of this framework motivates new multitask learning algorithms. We propose two new learning formulations by varying the parameters in the proposed framework. Empirical studies have revealed the relative advantages of the two new formulations by comparing with the state of the art, which provides instructive insights into the feature learning problem with multiple tasks.
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paper_title: Safe Screening for Multi-Task Feature Learning with Multiple Data Matrices

paper_content:

Multi-task feature learning (MTFL) is a powerful technique in boosting the predictive performance by learning multiple related classification/ regression/clustering tasks simultaneously. However, solving the MTFL problem remains challenging when the feature dimension is extremely large. In this paper, we propose a novel screening rule--that is based on the dual projection onto convex sets (DPC)--to quickly identify the inactive features--that have zero coefficients in the solution vectors across all tasks. One of the appealing features of DPC is that: it is safe in the sense that the detected inactive features are guaranteed to have zero coefficients in the solution vectors across all tasks. Thus, by removing the inactive features from the training phase, we may have substantial savings in the computational cost and memory usage without sacrificing accuracy. To the best of our knowledge, it is the first screening rule that is applicable to sparse models with multiple data matrices. A key challenge in deriving DPC is to solve a nonconvex problem. We show that we can solve for the global optimum efficiently via a properly chosen parametrization of the constraint set. Moreover, DPC has very low computational cost and can be integrated with any existing solvers. We have evaluated the proposed DPC rule on both synthetic and real data sets. The experiments indicate that DPC is very effective in identifying the inactive features--especially for high dimensional data--which leads to a speedup up to several orders of magnitude.
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paper_title: Joint covariate selection and joint subspace selection for multiple classification problems

paper_content:

We address the problem of recovering a common set of covariates that are relevant simultaneously to several classification problems. By penalizing the sum of ? 2 norms of the blocks of coefficients associated with each covariate across different classification problems, similar sparsity patterns in all models are encouraged. To take computational advantage of the sparsity of solutions at high regularization levels, we propose a blockwise path-following scheme that approximately traces the regularization path. As the regularization coefficient decreases, the algorithm maintains and updates concurrently a growing set of covariates that are simultaneously active for all problems. We also show how to use random projections to extend this approach to the problem of joint subspace selection, where multiple predictors are found in a common low-dimensional subspace. We present theoretical results showing that this random projection approach converges to the solution yielded by trace-norm regularization. Finally, we present a variety of experimental results exploring joint covariate selection and joint subspace selection, comparing the path-following approach to competing algorithms in terms of prediction accuracy and running time.
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paper_title: Trace Norm Regularization: Reformulations, Algorithms, and Multi-task Learning

paper_content:

We consider a recently proposed optimization formulation of multi-task learning based on trace norm regularized least squares. While this problem may be formulated as a semidefinite program (SDP), its size is beyond general SDP solvers. Previous solution approaches apply proximal gradient methods to solve the primal problem. We derive new primal and dual reformulations of this problem, including a reduced dual formulation that involves minimizing a convex quadratic function over an operator-norm ball in matrix space. This reduced dual problem may be solved by gradient-projection methods, with each projection involving a singular value decomposition. The dual approach is compared with existing approaches and its practical effectiveness is illustrated on simulations and an application to gene expression pattern analysis.
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paper_title: Flexible latent variable models for multi-task learning

paper_content:

Given multiple prediction problems such as regression or classification, we are interested in a joint inference framework that can effectively share information between tasks to improve the prediction accuracy, especially when the number of training examples per problem is small. In this paper we propose a probabilistic framework which can support a set of latent variable models for different multi-task learning scenarios. We show that the framework is a generalization of standard learning methods for single prediction problems and it can effectively model the shared structure among different prediction tasks. Furthermore, we present efficient algorithms for the empirical Bayes method as well as point estimation. Our experiments on both simulated datasets and real world classification datasets show the effectiveness of the proposed models in two evaluation settings: a standard multi-task learning setting and a transfer learning setting.
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paper_title: Multi-stage multi-task learning with reduced rank

paper_content:

Multi-task learning (MTL) seeks to improve the generalization performance by sharing information among multiple tasks. Many existing MTL approaches aim to learn the low-rank structure on the weight matrix, which stores the model parameters of all tasks, to achieve task sharing, and as a consequence the trace norm regularization is widely used in the MTL literature. A major limitation of these approaches based on trace norm regularization is that all the singular values of the weight matrix are penalized simultaneously, leading to impaired estimation on recovering the larger singular values in the weight matrix. To address the issue, we propose a Reduced rAnk MUlti-Stage multi-tAsk learning (RAMUSA) method based on the recently proposed capped norms. Different from existing trace-norm-based MTL approaches which minimize the sum of all the singular values, the RAMUSA method uses a capped trace norm regularizer to minimize only the singular values smaller than some threshold. Due to the non-convexity of the capped trace norm, we develop a simple but well guaranteed multi-stage algorithm to learn the weight matrix iteratively. We theoretically prove that the estimation error at each stage in the proposed algorithm shrinks and finally achieves a lower upper-bound as the number of stages becomes large enough. Empirical studies on synthetic and real-world datasets demonstrate the effectiveness of the RAMUSA method in comparison with the state-of-the-art methods.
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paper_title: Spectral k-Support Norm Regularization

paper_content:

The k-support norm has successfully been applied to sparse vector prediction problems. We observe that it belongs to a wider class of norms, which we call the box-norms. Within this framework we derive an efficient algorithm to compute the proximity operator of the squared norm, improving upon the original method for the k-support norm. We extend the norms from the vector to the matrix setting and we introduce the spectral k-support norm. We study its properties and show that it is closely related to the multitask learning cluster norm. We apply the norms to real and synthetic matrix completion datasets. Our findings indicate that spectral k-support norm regularization gives state of the art performance, consistently improving over trace norm regularization and the matrix elastic net.
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paper_title: Learning Multiple Related Tasks using Latent Independent Component Analysis

paper_content:

We propose a probabilistic model based on Independent Component Analysis for learning multiple related tasks. In our model the task parameters are assumed to be generated from independent sources which account for the relatedness of the tasks. We use Laplace distributions to model hidden sources which makes it possible to identify the hidden, independent components instead of just modeling correlations. Furthermore, our model enjoys a sparsity property which makes it both parsimonious and robust. We also propose efficient algorithms for both empirical Bayes method and point estimation. Our experimental results on two multi-label text classification data sets show that the proposed approach is promising.
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paper_title: A convex formulation for learning shared structures from multiple tasks

paper_content:

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. In this paper, we consider the problem of learning shared structures from multiple related tasks. We present an improved formulation (iASO) for multi-task learning based on the non-convex alternating structure optimization (ASO) algorithm, in which all tasks are related by a shared feature representation. We convert iASO, a non-convex formulation, into a relaxed convex one, which is, however, not scalable to large data sets due to its complex constraints. We propose an alternating optimization (cASO) algorithm which solves the convex relaxation efficiently, and further show that cASO converges to a global optimum. In addition, we present a theoretical condition, under which cASO can find a globally optimal solution to iASO. Experiments on several benchmark data sets confirm our theoretical analysis.
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paper_title: Spike and slab variational inference for multi-task and multiple kernel learning

paper_content:

We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi-task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multi-output Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.
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paper_title: A framework for learning predictive structures from multiple tasks and unlabeled data

paper_content:

One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting.
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paper_title: Sparse coding for multitask and transfer learning

paper_content:

We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear combinations of the atoms of a dictionary on a high or infinite dimensional space. This assumption, together with the large quantity of available data in the multitask and transfer learning settings, allows a principled choice of the dictionary. We provide bounds on the generalization error of this approach, for both settings. Numerical experiments on one synthetic and two real datasets show the advantage of our method over single task learning, a previous method based on orthogonal and dense representation of the tasks and a related method learning task grouping.
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paper_title: Discovering Structure in Multiple Learning Tasks: The TC Algorithm

paper_content:

Recently, there has been an increased interest in “lifelong” machine learning methods, that transfer knowledge across multiple learning tasks. Such methods have repeatedly been found to outperform conventional, single-task learning algorithms when the learning tasks are appropriately related. To increase robustness of such approaches, methods are desirable that can reason about the relatedness of individual learning tasks, in order to avoid the danger arising from tasks that are unrelated and thus potentially misleading. This paper describes the task-clustering (TC) algorithm. TC clusters learning tasks into classes of mutually related tasks. When facing a new learning task, TC first determines the most related task cluster, then exploits information selectively from this task cluster only. An empirical study carried out in a mobile robot domain shows that TC outperforms its non-selective counterpart in situations where only a small number of tasks is relevant.
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paper_title: The matrix stick-breaking process for flexible multi-task learning

paper_content:

In multi-task learning our goal is to design regression or classification models for each of the tasks and appropriately share information between tasks. A Dirichlet process (DP) prior can be used to encourage task clustering. However, the DP prior does not allow local clustering of tasks with respect to a subset of the feature vector without making independence assumptions. Motivated by this problem, we develop a new multitask-learning prior, termed the matrix stick-breaking process (MSBP), which encourages cross-task sharing of data. However, the MSBP allows separate clustering and borrowing of information for the different feature components. This is important when tasks are more closely related for certain features than for others. Bayesian inference proceeds by a Gibbs sampling algorithm and the approach is illustrated using a simulated example and a multi-national application.
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paper_title: Multi-task learning for sequential data via iHMMs and the nested Dirichlet process

paper_content:

A new hierarchical nonparametric Bayesian model is proposed for the problem of multitask learning (MTL) with sequential data. Sequential data are typically modeled with a hidden Markov model (HMM), for which one often must choose an appropriate model structure (number of states) before learning. Here we model sequential data from each task with an infinite hidden Markov model (iHMM), avoiding the problem of model selection. The MTL for iHMMs is implemented by imposing a nested Dirichlet process (nDP) prior on the base distributions of the iHMMs. The nDP-iHMM MTL method allows us to perform task-level clustering and data-level clustering simultaneously, with which the learning for individual iHMMs is enhanced and between-task similarities are learned. Learning and inference for the nDP-iHMM MTL are based on a Gibbs sampler. The effectiveness of the framework is demonstrated using synthetic data as well as real music data.
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paper_title: Convex multi-task feature learning

paper_content:

We present a method for learning sparse representations shared across multiple tasks. This method is a generalization of the well-known single-task 1-norm regularization. It is based on a novel non-convex regularizer which controls the number of learned features common across the tasks. We prove that the method is equivalent to solving a convex optimization problem for which there is an iterative algorithm which converges to an optimal solution. The algorithm has a simple interpretation: it alternately performs a supervised and an unsupervised step, where in the former step it learns task-specific functions and in the latter step it learns common-across-tasks sparse representations for these functions. We also provide an extension of the algorithm which learns sparse nonlinear representations using kernels. We report experiments on simulated and real data sets which demonstrate that the proposed method can both improve the performance relative to learning each task independently and lead to a few learned features common across related tasks. Our algorithm can also be used, as a special case, to simply select--not learn--a few common variables across the tasks.
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paper_title: Learning Gaussian processes from multiple tasks

paper_content:

We consider the problem of multi-task learning, that is, learning multiple related functions. Our approach is based on a hierarchical Bayesian framework, that exploits the equivalence between parametric linear models and nonparametric Gaussian processes (GPs). The resulting models can be learned easily via an EM-algorithm. Empirical studies on multi-label text categorization suggest that the presented models allow accurate solutions of these multi-task problems.
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paper_title: Nonparametric Bayesian feature selection for multi-task learning

paper_content:

We present a nonparametric Bayesian model for multi-task learning, with a focus on feature selection in binary classification. The model jointly identifies groups of similar tasks and selects the subset of features relevant to the tasks within each group. The model employs a Dirchlet process with a beta- Bernoulli hierarchical base measure. The posterior inference is accomplished efficiently using a Gibbs sampler. Experimental results are presented on simulated as well as real data.
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paper_title: Convex Multi-Task Learning by Clustering

paper_content:

We consider the problem of multi-task learning in which tasks belong to hidden clusters. We formulate the learning problem as a novel convex optimization problem in which linear classiers are combinations of (a small number of) some basis. Our formulation jointly learns both the basis and the linear combination. We propose a scalable optimization algorithm for nding the optimal solution. Our new methods outperform existing stateof-the-art methods on multi-task sentiment classication tasks.
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paper_title: Adaptive Multi-Task Lasso: with application to eQTL detection

paper_content:

To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects. However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared to the number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. ::: ::: In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively. Then we find the maximum a posteriori (MAP) estimation of regression coefficients and estimate weights of covariates jointly. This optimization procedure is efficient since it can be achieved by using a projected gradient descent and a coordinate descent procedure iteratively. Experimental results on simulated and real yeast datasets confirm that our model outperforms previous methods for finding eQTLs.
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paper_title: Learning with Whom to Share in Multi-task Feature Learning

paper_content:

In multi-task learning (MTL), multiple tasks are learnt jointly. A major assumption for this paradigm is that all those tasks are indeed related so that the joint training is appropriate and beneficial. In this paper, we study the problem of multi-task learning of shared feature representations among tasks, while simultaneously determining "with whom" each task should share. We formulate the problem as a mixed integer programming and provide an alternating minimization technique to solve the optimization problem of jointly identifying grouping structures and parameters. The algorithm mono-tonically decreases the objective function and converges to a local optimum. Compared to the standard MTL paradigm where all tasks are in a single group, our algorithm improves its performance with statistical significance for three out of the four datasets we have studied. We also demonstrate its advantage over other task grouping techniques investigated in literature.
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paper_title: Multi-Task Learning for Analyzing and Sorting Large Databases of Sequential Data

paper_content:

A new hierarchical nonparametric Bayesian framework is proposed for the problem of multi-task learning (MTL) with sequential data. The models for multiple tasks, each characterized by sequential data, are learned jointly, and the intertask relationships are obtained simultaneously. This MTL setting is used to analyze and sort large databases composed of sequential data, such as music clips. Within each data set, we represent the sequential data with an infinite hidden Markov model (iHMM), avoiding the problem of model selection (selecting a number of states). Across the data sets, the multiple iHMMs are learned jointly in a MTL setting, employing a nested Dirichlet process (nDP). The nDP-iHMM MTL method allows simultaneous task-level and data-level clustering, with which the individual iHMMs are enhanced and the between-task similarities are learned. Therefore, in addition to improved learning of each of the models via appropriate data sharing, the learned sharing mechanisms are used to infer interdata relationships of interest for data search. Specifically, the MTL-learned task-level sharing mechanisms are used to define the affinity matrix in a graph-diffusion sorting framework. To speed up the MCMC inference for large databases, the nDP-iHMM is truncated to yield a nested Dirichlet-distribution based HMM representation, which accommodates fast variational Bayesian (VB) analysis for large-scale inference, and the effectiveness of the framework is demonstrated using a database composed of 2500 digital music pieces.
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paper_title: Clustered Multi-Task Learning: A Convex Formulation

paper_content:

In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions for supervised classification or regression, this can be achieved by including a priori information about the weight vectors associated with the tasks, and how they are expected to be related to each other. In this paper, we assume that tasks are clustered into groups, which are unknown beforehand, and that tasks within a group have similar weight vectors. We design a new spectral norm that encodes this a priori assumption, without the prior knowledge of the partition of tasks into groups, resulting in a new convex optimization formulation for multi-task learning. We show in simulations on synthetic examples and on the IEDB MHC-I binding dataset, that our approach outperforms well-known convex methods for multi-task learning, as well as related non-convex methods dedicated to the same problem.
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paper_title: Task Clustering and Gating for Bayesian Multitask Learning

paper_content:

Modeling a collection of similar regression or classification tasks can be improved by making the tasks 'learn from each other'. In machine learning, this subject is approached through 'multitask learning', where parallel tasks are modeled as multiple outputs of the same network. In multilevel analysis this is generally implemented through the mixed-effects linear model where a distinction is made between 'fixed effects', which are the same for all tasks, and 'random effects', which may vary between tasks. In the present article we will adopt a Bayesian approach in which some of the model parameters are shared (the same for all tasks) and others more loosely connected through a joint prior distribution that can be learned from the data. We seek in this way to combine the best parts of both the statistical multilevel approach and the neural network machinery. The standard assumption expressed in both approaches is that each task can learn equally well from any other task. In this article we extend the model by allowing more differentiation in the similarities between tasks. One such extension is to make the prior mean depend on higher-level task characteristics. More unsupervised clustering of tasks is obtained if we go from a single Gaussian prior to a mixture of Gaussians. This can be further generalized to a mixture of experts architecture with the gates depending on task characteristics. All three extensions are demonstrated through application both on an artificial data set and on two real-world problems, one a school problem and the other involving single-copy newspaper sales.
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paper_title: Multi-task compressive sensing with Dirichlet process priors

paper_content:

Compressive sensing (CS) is an emerging £eld that, under appropriate conditions, can signi£cantly reduce the number of measurements required for a given signal. In many applications, one is interested in multiple signals that may be measured in multiple CS-type measurements, where here each signal corresponds to a sensing "task". In this paper we propose a novel multitask compressive sensing framework based on a Bayesian formalism, where a Dirichlet process (DP) prior is employed, yielding a principled means of simultaneously inferring the appropriate sharing mechanisms as well as CS inversion for each task. A variational Bayesian (VB) inference algorithm is employed to estimate the full posterior on the model parameters.
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paper_title: A Multitask Point Process Predictive Model

paper_content:

Point process data are commonly observed in fields like healthcare and the social sciences. Designing predictive models for such event streams is an under-explored problem, due to often scarce training data. In this work we propose a multitask point process model, leveraging information from all tasks via a hierarchical Gaussian process (GP). Nonparametric learning functions implemented by a GP, which map from past events to future rates, allow analysis of flexible arrival patterns. To facilitate efficient inference, we propose a sparse construction for this hierarchical model, and derive a variational Bayes method for learning and inference. Experimental results are shown on both synthetic data and as well as real electronic health-records data.
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paper_title: Learning multi-level task groups in multi-task learning

paper_content:

In multi-task learning (MTL), multiple related tasks are learned jointly by sharing information across them. Many MTL algorithms have been proposed to learn the underlying task groups. However, those methods are limited to learn the task groups at only a single level, which may be not sufficient to model the complex structure among tasks in many real-world applications. In this paper, we propose a Multi-Level Task Grouping (MeTaG) method to learn the multi-level grouping structure instead of only one level among tasks. Specifically, by assuming the number of levels to be H, we decompose the parameter matrix into a sum of H component matrices, each of which is regularized with a l2 norm on the pairwise difference among parameters of all the tasks to construct level-specific task groups. For optimization, we employ the smoothing proximal gradient method to efficiently solve the objective function of the MeTaG model. Moreover, we provide theoretical analysis to show that under certain conditions the MeTaG model can recover the true parameter matrix and the true task groups in each level with high probability. We experiment our approach on both synthetic and real-world datasets, showing competitive performance over state-of-the-art MTL methods.
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paper_title: Flexible Clustered Multi-Task Learning by Learning Representative Tasks

paper_content:

Multi-task learning (MTL) methods have shown promising performance by learning multiple relevant tasks simultaneously, which exploits to share useful information across relevant tasks. Among various MTL methods, clustered multi-task learning (CMTL) assumes that all tasks can be clustered into groups and attempts to learn the underlying cluster structure from the training data. In this paper, we present a new approach for CMTL, called flexible clustered multi-task (FCMTL), in which the cluster structure is learned by identifying representative tasks. The new approach allows an arbitrary task to be described by multiple representative tasks, effectively soft-assigning a task to multiple clusters with different weights. Unlike existing counterpart, the proposed approach is more flexible in that (a) it does not require clusters to be disjoint, (b) tasks within one particular cluster do not have to share information to the same extent, and (c) the number of clusters is automatically inferred from data. Computationally, the proposed approach is formulated as a row-sparsity pursuit problem. We validate the proposed FCMTL on both synthetic and real-world data sets, and empirical results demonstrate that it outperforms many existing MTL methods.
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paper_title: A framework for learning predictive structures from multiple tasks and unlabeled data

paper_content:

One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting.
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paper_title: Multi-task learning for classification with dirichlet process priors

paper_content:

Consider the problem of learning logistic-regression models for multiple classification tasks, where the training data set for each task is not drawn from the same statistical distribution. In such a multi-task learning (MTL) scenario, it is necessary to identify groups of similar tasks that should be learned jointly. Relying on a Dirichlet process (DP) based statistical model to learn the extent of similarity between classification tasks, we develop computationally efficient algorithms for two different forms of the MTL problem. First, we consider a symmetric multi-task learning (SMTL) situation in which classifiers for multiple tasks are learned jointly using a variational Bayesian (VB) algorithm. Second, we consider an asymmetric multi-task learning (AMTL) formulation in which the posterior density function from the SMTL model parameters (from previous tasks) is used as a prior for a new task: this approach has the significant advantage of not requiring storage and use of all previous data from prior tasks. The AMTL formulation is solved with a simple Markov Chain Monte Carlo (MCMC) construction. Experimental results on two real life MTL problems indicate that the proposed algorithms: (a) automatically identify subgroups of related tasks whose training data appear to be drawn from similar distributions; and (b) are more accurate than simpler approaches such as single-task learning, pooling of data across all tasks, and simplified approximations to DP.
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paper_title: Regularized multi--task learning

paper_content:

Past empirical work has shown that learning multiple related tasks from data simultaneously can be advantageous in terms of predictive performance relative to learning these tasks independently. In this paper we present an approach to multi--task learning based on the minimization of regularization functionals similar to existing ones, such as the one for Support Vector Machines (SVMs), that have been successfully used in the past for single--task learning. Our approach allows to model the relation between tasks in terms of a novel kernel function that uses a task--coupling parameter. We implement an instance of the proposed approach similar to SVMs and test it empirically using simulated as well as real data. The experimental results show that the proposed method performs better than existing multi--task learning methods and largely outperforms single--task learning using SVMs.
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paper_title: Multilabel relationship learning

paper_content:

Multilabel learning problems are commonly found in many applications. A characteristic shared by many multilabel learning problems is that some labels have significant correlations between them. In this article, we propose a novel multilabel learning method, called MultiLabel Relationship Learning (MLRL), which extends the conventional support vector machine by explicitly learning and utilizing the relationships between labels. Specifically, we model the label relationships using a label covariance matrix and use it to define a new regularization term for the optimization problem. MLRL learns the model parameters and the label covariance matrix simultaneously based on a unified convex formulation. To solve the convex optimization problem, we use an alternating method in which each subproblem can be solved efficiently. The relationship between MLRL and two widely used maximum margin methods for multilabel learning is investigated. Moreover, we also propose a semisupervised extension of MLRL, called SSMLRL, to demonstrate how to make use of unlabeled data to help learn the label covariance matrix. Through experiments conducted on some multilabel applications, we find that MLRL not only gives higher classification accuracy but also has better interpretability as revealed by the label covariance matrix.
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paper_title: Multi-task sparse structure learning with Gaussian copula models

paper_content:

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. While sometimes the underlying task relationship structure is known, often the structure needs to be estimated from data at hand. In this paper, we present a novel family of models for MTL, applicable to regression and classification problems, capable of learning the structure of tasks relationship. In particular, we consider a joint estimation problem of the tasks relationship structure and the individual task parameters, which is solved using alternating minimization. The task relationship revealed by structure learning is founded on recent advances in Gaussian graphical models endowed with sparse estimators of the precision (inverse covariance) matrix. An extension to include exible Gaussian copula models that relaxes the Gaussian marginal assumption is also proposed. We illustrate the effectiveness of the proposed model on a variety of synthetic and benchmark data sets for regression and classification. We also consider the problem of combining Earth System Model (ESM) outputs for better projections of future climate, with focus on projections of temperature by combining ESMs in South and North America, and show that the proposed model outperforms several existing methods for the problem.
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paper_title: Learning High-Order Task Relationships in MultiTask Learning

paper_content:

Multi-task learning is a way of bringing inductive transfer studied in human learning to the machine learning community. A central issue in multitask learning is to model the relationships between tasks appropriately and exploit them to aid the simultaneous learning of multiple tasks effectively. While some recent methods model and learn the task relationships from data automatically, only pairwise relationships can be represented by them. In this paper, we propose a new model, called Multi-Task High-Order relationship Learning (MTHOL), which extends in a novel way the use of pairwise task relationships to high-order task relationships. We first propose an alternative formulation of an existing multi-task learning method. Based on the new formulation, we propose a high-order generalization leading to a new prior for the model parameters of different tasks. We then propose a new probabilistic model for multi-task learning and validate it empirically on some benchmark datasets.
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paper_title: Learning Multiple Tasks with Kernel Methods

paper_content:

We study the problem of learning many related tasks simultaneously using kernel methods and regularization. The standard single-task kernel methods, such as support vector machines and regularization networks, are extended to the case of multi-task learning. Our analysis shows that the problem of estimating many task functions with regularization can be cast as a single task learning problem if a family of multi-task kernel functions we define is used. These kernels model relations among the tasks and are derived from a novel form of regularizers. Specific kernels that can be used for multi-task learning are provided and experimentally tested on two real data sets. In agreement with past empirical work on multi-task learning, the experiments show that learning multiple related tasks simultaneously using the proposed approach can significantly outperform standard single-task learning particularly when there are many related tasks but few data per task.
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paper_title: Multi-Task Boosting by Exploiting Task Relationships

paper_content:

Multi-task learning aims at improving the performance of one learning task with the help of other related tasks. It is particularly useful when each task has very limited labeled data. A central issue in multi-task learning is to learn and exploit the relationships between tasks. In this paper, we generalize boosting to the multi-task learning setting and propose a method called multi-task boosting (MTBoost). Different tasks in MTBoost share the same base learners but with different weights which are related to the estimated task relationships in each iteration. In MTBoost, unlike ordinary boosting methods, the base learners, weights and task covariances are learned together in an integrated fashion using an alternating optimization procedure. We conduct theoretical analysis on the convergence of MTBoost and also empirical analysis comparing it with several related methods.
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paper_title: Asymmetric multi-task learning based on task relatedness and loss

paper_content:

We propose a novel multi-task learning method that minimizes the effect of negative transfer by allowing asymmetric transfer between the tasks based on task relatedness as well as the amount of individual task losses, which we refer to as Asymmetric Multi-task Learning (AMTL). To tackle this problem, we couple multiple tasks via a sparse, directed regularization graph, that enforces each task parameter to be reconstructed as a sparse combination of other tasks selected based on the task-wise loss. We present two different algorithms that jointly learn the task predictors as well as the regularization graph. The first algorithm solves for the original learning objective using alternative optimization, and the second algorithm solves an approximation of it using curriculum learning strategy, that learns one task at a time. We perform experiments on multiple datasets for classification and regression, on which we obtain significant improvements in performance over the single task learning and existing multitask learning models.
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paper_title: A Convex Formulation for Learning Task Relationships in Multi-Task Learning

paper_content:

Multi-task learning is a learning paradigm which seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this paper, we propose a regularization formulation for learning the relationships between tasks in multi-task learning. This formulation can be viewed as a novel generalization of the regularization framework for single-task learning. Besides modeling positive task correlation, our method, called multi-task relationship learning (MTRL), can also describe negative task correlation and identify outlier tasks based on the same underlying principle. Under this regularization framework, the objective function of MTRL is convex. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multi-task learning setting and then generalize it to the asymmetric setting as well. We also study the relationships between MTRL and some existing multi-task learning methods. Experiments conducted on a toy problem as well as several benchmark data sets demonstrate the effectiveness of MTRL.
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paper_title: Large margin multi-task metric learning

paper_content:

Multi-task learning (MTL) improves the prediction performance on multiple, different but related, learning problems through shared parameters or representations. One of the most prominent multi-task learning algorithms is an extension to support vector machines (svm) by Evgeniou et al. [15]. Although very elegant, multi-task svm is inherently restricted by the fact that support vector machines require each class to be addressed explicitly with its own weight vector which, in a multi-task setting, requires the different learning tasks to share the same set of classes. This paper proposes an alternative formulation for multi-task learning by extending the recently published large margin nearest neighbor (1mnn) algorithm to the MTL paradigm. Instead of relying on separating hyperplanes, its decision function is based on the nearest neighbor rule which inherently extends to many classes and becomes a natural fit for multi-task learning. We evaluate the resulting multi-task 1mnn on real-world insurance data and speech classification problems and show that it consistently outperforms single-task kNN under several metrics and state-of-the-art MTL classifiers.
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paper_title: Multi-Task Learning with Gaussian Matrix Generalized Inverse Gaussian Model

paper_content:

In this paper, we study the multi-task learning problem with a new perspective of considering the structure of the residue error matrix and the low-rank approximation to the task covariance matrix simultaneously. In particular, we first introduce the Matrix Generalized Inverse Gaussian (MGIG) prior and define a Gaussian Matrix Generalized Inverse Gaussian (GMGIG) model for low-rank approximation to the task covariance matrix. Through combining the GMGIG model with the residual error structure assumption, we propose the GMGIG regression model for multi-task learning. To make the computation tractable, we simultaneously use variational inference and sampling techniques. In particular, we propose two sampling strategies for computing the statistics of the MGIG distribution. Experiments show that this model is superior to the peer methods in regression and prediction.
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paper_title: Simultaneously Leveraging Output and Task Structures for Multiple-Output Regression

paper_content:

Multiple-output regression models require estimating multiple parameters, one for each output. Structural regularization is usually employed to improve parameter estimation in such models. In this paper, we present a multiple-output regression model that leverages the covariance structure of the latent model parameters as well as the conditional covariance structure of the observed outputs. This is in contrast with existing methods that usually take into account only one of these structures. More importantly, unlike some of the other existing methods, none of these structures need be known a priori in our model, and are learned from the data. Several previously proposed structural regularization based multiple-output regression models turn out to be special cases of our model. Moreover, in addition to being a rich model for multiple-output regression, our model can also be used in estimating the graphical model structure of a set of variables (multivariate outputs) conditioned on another set of variables (inputs). Experimental results on both synthetic and real datasets demonstrate the effectiveness of our method.
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paper_title: Efficient Output Kernel Learning for Multiple Tasks

paper_content:

The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other. While previously the relationship between tasks had to be user-defined in the form of an output kernel, recent approaches jointly learn the tasks and the output kernel. As the output kernel is a positive semidefinite matrix, the resulting optimization problems are not scalable in the number of tasks as an eigendecomposition is required in each step. Using the theory of positive semidefinite kernels we show in this paper that for a certain class of regularizers on the output kernel, the constraint of being positive semidefinite can be dropped as it is automatically satisfied for the relaxed problem. This leads to an unconstrained dual problem which can be solved efficiently. Experiments on several multi-task and multi-class data sets illustrate the efficacy of our approach in terms of computational efficiency as well as generalization performance.
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paper_title: A Kernel Method for the Two-Sample Problem

paper_content:

We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS). We present two tests based on large deviation bounds for the test statistic, while a third is based on the asymptotic distribution of this statistic. The test statistic can be computed in quadratic time, although efficient linear time approximations are available. Several classical metrics on distributions are recovered when the function space used to compute the difference in expectations is allowed to be more general (eg. a Banach space). We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.
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paper_title: Hierarchical Multitask Structured Output Learning for Large-Scale Sequence Segmentation

paper_content:

We present a novel regularization-based Multitask Learning (MTL) formulation for Structured Output (SO) prediction for the case of hierarchical task relations. Structured output prediction often leads to difficult inference problems and hence requires large amounts of training data to obtain accurate models. We propose to use MTL to exploit additional information from related learning tasks by means of hierarchical regularization. Training SO models on the combined set of examples from multiple tasks can easily become infeasible for real world applications. To be able to solve the optimization problems underlying multitask structured output learning, we propose an efficient algorithm based on bundle-methods. We demonstrate the performance of our approach in applications from the domain of computational biology addressing the key problem of gene finding. We show that 1) our proposed solver achieves much faster convergence than previous methods and 2) that the Hierarchical SO-MTL approach outperforms considered non-MTL methods.
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paper_title: Multi-Stage Multi-Task Feature Learning

paper_content:

Multi-task sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. Most of the existing multi-task sparse feature learning algorithms are formulated as a convex sparse regularization problem, which is usually suboptimal, due to its looseness for approximating an l0-type regularizer. In this paper, we propose a non-convex formulation for multi-task sparse feature learning based on a novel nonconvex regularizer. To solve the non-convex optimization problem, we propose a Multi-Stage Multi-Task Feature Learning (MSMTFL) algorithm; we also provide intuitive interpretations, detailed convergence and reproducibility analysis for the proposed algorithm. Moreover, we present a detailed theoretical analysis showing that MSMTFL achieves a better parameter estimation error bound than the convex formulation. Empirical studies on both synthetic and real-world data sets demonstrate the effectiveness of MSMTFL in comparison with the state of the art multi-task sparse feature learning algorithms.
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paper_title: Generalization Errors and Learning Curves for Regression with Multi-task Gaussian Processes

paper_content:

We provide some insights into how task correlations in multi-task Gaussian process (GP) regression affect the generalization error and the learning curve. We analyze the asymmetric two-tasks case, where a secondary task is to help the learning of a primary task. Within this setting, we give bounds on the generalization error and the learning curve of the primary task. Our approach admits intuitive understandings of the multi-task GP by relating it to single-task GPs. For the case of one-dimensional input-space under optimal sampling with data only for the secondary task, the limitations of multi-task GP can be quantified explicitly.
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paper_title: Efficient multi-task feature learning with calibration

paper_content:

Multi-task feature learning has been proposed to improve the generalization performance by learning the shared features among multiple related tasks and it has been successfully applied to many real-world problems in machine learning, data mining, computer vision and bioinformatics. Most existing multi-task feature learning models simply assume a common noise level for all tasks, which may not be the case in real applications. Recently, a Calibrated Multivariate Regression (CMR) model has been proposed, which calibrates different tasks with respect to their noise levels and achieves superior prediction performance over the non-calibrated one. A major challenge is how to solve the CMR model efficiently as it is formulated as a composite optimization problem consisting of two non-smooth terms. In this paper, we propose a variant of the calibrated multi-task feature learning formulation by including a squared norm regularizer. We show that the dual problem of the proposed formulation is a smooth optimization problem with a piecewise sphere constraint. The simplicity of the dual problem enables us to develop fast dual optimization algorithms with low per-iteration cost. We also provide a detailed convergence analysis for the proposed dual optimization algorithm. Empirical studies demonstrate that, the dual optimization algorithm quickly converges and it is much more efficient than the primal optimization algorithm. Moreover, the calibrated multi-task feature learning algorithms with and without the squared norm regularizer achieve similar prediction performance and both outperform the non-calibrated ones. Thus, the proposed variant not only enables us to develop fast optimization algorithms, but also keeps the superior prediction performance of the calibrated multi-task feature learning over the non-calibrated one.
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paper_title: Convex Learning of Multiple Tasks and their Structure

paper_content:

Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context a fundamental question is how to incorporate the tasks structure in the learning problem. We tackle this question by studying a general computational framework that allows to encode apriori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches. Within this framework, we show that tasks and their structure can be efficiently learned considering a convex optimization problem that can be approached by means of block coordinate methods such as alternating minimization and for which we prove convergence to the global minimum.
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paper_title: A Regularization Approach to Learning Task Relationships in Multitask Learning

paper_content:

Multitask learning is a learning paradigm that seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this article, we propose a regularization approach to learning the relationships between tasks in multitask learning. This approach can be viewed as a novel generalization of the regularized formulation for single-task learning. Besides modeling positive task correlation, our approach—multitask relationship learning (MTRL)—can also describe negative task correlation and identify outlier tasks based on the same underlying principle. By utilizing a matrix-variate normal distribution as a prior on the model parameters of all tasks, our MTRL method has a jointly convex objective function. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multitask learning setting and then generalize it to the asymmetric setting as well. We also discuss some variants of the regularization approach to demonstrate the use of other matrix-variate priors for learning task relationships. Moreover, to gain more insight into our model, we also study the relationships between MTRL and some existing multitask learning methods. Experiments conducted on a toy problem as well as several benchmark datasets demonstrate the effectiveness of MTRL as well as its high interpretability revealed by the task covariance matrix.
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paper_title: Learning Output Kernels with Block Coordinate Descent

paper_content:

We propose a method to learn simultaneously a vector-valued function and a kernel between its components. The obtained kernel can be used both to improve learning performance and to reveal structures in the output space which may be important in their own right. Our method is based on the solution of a suitable regularization problem over a reproducing kernel Hilbert space of vector-valued functions. Although the regularized risk functional is non-convex, we show that it is invex, implying that all local minimizers are global minimizers. We derive a block-wise coordinate descent method that efficiently exploits the structure of the objective functional. Then, we empirically demonstrate that the proposed method can improve classification accuracy. Finally, we provide a visual interpretation of the learned kernel matrix for some well known datasets.
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paper_title: Conic Programming for Multitask Learning

paper_content:

When we have several related tasks, solving them simultaneously has been shown to be more effective than solving them individually. This approach is called multitask learning (MTL). In this paper, we propose a novel MTL algorithm. Our method controls the relatedness among the tasks locally, so all pairs of related tasks are guaranteed to have similar solutions. We apply the above idea to support vector machines and show that the optimization problem can be cast as a second-order cone program, which is convex and can be solved efficiently. The usefulness of our approach is demonstrated in ordinal regression, link prediction, and collaborative filtering, each of which can be formulated as a structured multitask problem.
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paper_title: Multi-task Gaussian Process Prediction

paper_content:

In this paper we investigate multi-task learning in the context of Gaussian Processes (GP). We propose a model that learns a shared covariance function on input-dependent features and a "free-form" covariance matrix over tasks. This allows for good flexibility when modelling inter-task dependencies while avoiding the need for large amounts of data for training. We show that under the assumption of noise-free observations and a block design, predictions for a given task only depend on its target values and therefore a cancellation of inter-task transfer occurs. We evaluate the benefits of our model on two practical applications: a compiler performance prediction problem and an exam score prediction task. Additionally, we make use of GP approximations and properties of our model in order to provide scalability to large data sets.
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paper_title: Heterogeneous-Neighborhood-based Multi-Task Local Learning Algorithms

paper_content:

All the existing multi-task local learning methods are defined on homogeneous neighborhood which consists of all data points from only one task. In this paper, different from existing methods, we propose local learning methods for multitask classification and regression problems based on heterogeneous neighborhood which is defined on data points from all tasks. Specifically, we extend the k-nearest-neighbor classifier by formulating the decision function for each data point as a weighted voting among the neighbors from all tasks where the weights are task-specific. By defining a regularizer to enforce the task-specific weight matrix to approach a symmetric one, a regularized objective function is proposed and an efficient coordinate descent method is developed to solve it. For regression problems, we extend the kernel regression to multi-task setting in a similar way to the classification case. Experiments on some toy data and real-world datasets demonstrate the effectiveness of our proposed methods.
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paper_title: Learning multiple visual tasks while discovering their structure

paper_content:

Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to name a few. The key idea is that exploring task relatedness (structure) can lead to improved performances. In this paper, we propose and study a novel sparse, nonparametric approach exploiting the theory of Reproducing Kernel Hilbert Spaces for vector-valued functions. We develop a suitable regularization framework which can be formulated as a convex optimization problem, and is provably solvable using an alternating minimization approach. Empirical tests show that the proposed method compares favorably to state of the art techniques and further allows to recover interpretable structures, a problem of interest in its own right.
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paper_title: It is all in the noise: Efficient multi-task Gaussian process inference with structured residuals

paper_content:

Multi-task prediction methods are widely used to couple regressors or classification models by sharing information across related tasks. We propose a multi-task Gaussian process approach for modeling both the relatedness between regressors and the task correlations in the residuals, in order to more accurately identify true sharing between regressors. The resulting Gaussian model has a covariance term in form of a sum of Kronecker products, for which efficient parameter inference and out of sample prediction are feasible. On both synthetic examples and applications to phenotype prediction in genetics, we find substantial benefits of modeling structured noise compared to established alternatives.
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paper_title: Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

paper_content:

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multitask learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is nonconvex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose employing the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is nondifferentiable and the feasible domain is nontrivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of the projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and a Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in detail. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multitask learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multitask learning formulation and the efficiency of the proposed projected gradient algorithms.
---
paper_title: Convex Multitask Learning with Flexible Task Clusters

paper_content:

Traditionally, multitask learning (MTL) assumes that all the tasks are related. This can lead to negative transfer when tasks are indeed incoherent. Recently, a number of approaches have been proposed that alleviate this problem by discovering the underlying task clusters or relationships. However, they are limited to modeling these relationships at the task level, which may be restrictive in some applications. In this paper, we propose a novel MTL formulation that captures task relationships at the feature-level. Depending on the interactions among tasks and features, the proposed method construct different task clusters for different features, without even the need of pre-specifying the number of clusters. Computationally, the proposed formulation is strongly convex, and can be efficiently solved by accelerated proximal methods. Experiments are performed on a number of synthetic and real-world data sets. Under various degrees of task relationships, the accuracy of the proposed method is consistently among the best. Moreover, the feature-specific task clusters obtained agree with the known/plausible task structures of the data.
---
paper_title: Integrating low-rank and group-sparse structures for robust multi-task learning

paper_content:

Multi-task learning (MTL) aims at improving the generalization performance by utilizing the intrinsic relationships among multiple related tasks. A key assumption in most MTL algorithms is that all tasks are related, which, however, may not be the case in many real-world applications. In this paper, we propose a robust multi-task learning (RMTL) algorithm which learns multiple tasks simultaneously as well as identifies the irrelevant (outlier) tasks. Specifically, the proposed RMTL algorithm captures the task relationships using a low-rank structure, and simultaneously identifies the outlier tasks using a group-sparse structure. The proposed RMTL algorithm is formulated as a non-smooth convex (unconstrained) optimization problem. We propose to adopt the accelerated proximal method (APM) for solving such an optimization problem. The key component in APM is the computation of the proximal operator, which can be shown to admit an analytic solution. We also theoretically analyze the effectiveness of the RMTL algorithm. In particular, we derive a key property of the optimal solution to RMTL; moreover, based on this key property, we establish a theoretical bound for characterizing the learning performance of RMTL. Our experimental results on benchmark data sets demonstrate the effectiveness and efficiency of the proposed algorithm.
---
paper_title: A Dirty Model for Multi-task Learning

paper_content:

We consider multi-task learning in the setting of multiple linear regression, and where some relevant features could be shared across the tasks. Recent research has studied the use of l1/lq norm block-regularizations with q > 1 for such block-sparse structured problems, establishing strong guarantees on recovery even under high-dimensional scaling where the number of features scale with the number of observations. However, these papers also caution that the performance of such block-regularized methods are very dependent on the extent to which the features are shared across tasks. Indeed they show [8] that if the extent of overlap is less than a threshold, or even if parameter values in the shared features are highly uneven, then block l1/lq regularization could actually perform worse than simple separate elementwise l1 regularization. Since these caveats depend on the unknown true parameters, we might not know when and which method to apply. Even otherwise, we are far away from a realistic multi-task setting: not only do the set of relevant features have to be exactly the same across tasks, but their values have to as well. ::: ::: Here, we ask the question: can we leverage parameter overlap when it exists, but not pay a penalty when it does not? Indeed, this falls under a more general question of whether we can model such dirty data which may not fall into a single neat structural bracket (all block-sparse, or all low-rank and so on). With the explosion of such dirty high-dimensional data in modern settings, it is vital to develop tools - dirty models - to perform biased statistical estimation tailored to such data. Here, we take a first step, focusing on developing a dirty model for the multiple regression problem. Our method uses a very simple idea: we estimate a superposition of two sets of parameters and regularize them differently. We show both theoretically and empirically, our method strictly and noticeably outperforms both l1 or l1/lq methods, under high-dimensional scaling and over the entire range of possible overlaps (except at boundary cases, where we match the best method).
---
paper_title: Multi-level Lasso for Sparse Multi-task Regression

paper_content:

We present a flexible formulation for variable selection in multi-task regression to allow for discrepancies in the estimated sparsity patterns accross the multiple tasks, while leveraging the common structure among them. Our approach is based on an intuitive decomposition of the regression coe_cients into a product between a component that is common to all tasks and another component that captures task-specificity. This decomposition yields the Multi-level Lasso objective that can be solved efficiently via alternating optimization. The analysis of the "orthonormal design" case reveals some interesting insights on the nature of the shrinkage performed by our method, compared to that of related work. Theoretical guarantees are provided on the consistency of Multi-level Lasso. Simulations and empirical study of micro-array data further demonstrate the value of our framework.
---
paper_title: Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

paper_content:

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multitask learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is nonconvex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose employing the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is nondifferentiable and the feasible domain is nontrivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of the projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and a Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in detail. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multitask learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multitask learning formulation and the efficiency of the proposed projected gradient algorithms.
---
paper_title: Convex Multitask Learning with Flexible Task Clusters

paper_content:

Traditionally, multitask learning (MTL) assumes that all the tasks are related. This can lead to negative transfer when tasks are indeed incoherent. Recently, a number of approaches have been proposed that alleviate this problem by discovering the underlying task clusters or relationships. However, they are limited to modeling these relationships at the task level, which may be restrictive in some applications. In this paper, we propose a novel MTL formulation that captures task relationships at the feature-level. Depending on the interactions among tasks and features, the proposed method construct different task clusters for different features, without even the need of pre-specifying the number of clusters. Computationally, the proposed formulation is strongly convex, and can be efficiently solved by accelerated proximal methods. Experiments are performed on a number of synthetic and real-world data sets. Under various degrees of task relationships, the accuracy of the proposed method is consistently among the best. Moreover, the feature-specific task clusters obtained agree with the known/plausible task structures of the data.
---
paper_title: Integrating low-rank and group-sparse structures for robust multi-task learning

paper_content:

Multi-task learning (MTL) aims at improving the generalization performance by utilizing the intrinsic relationships among multiple related tasks. A key assumption in most MTL algorithms is that all tasks are related, which, however, may not be the case in many real-world applications. In this paper, we propose a robust multi-task learning (RMTL) algorithm which learns multiple tasks simultaneously as well as identifies the irrelevant (outlier) tasks. Specifically, the proposed RMTL algorithm captures the task relationships using a low-rank structure, and simultaneously identifies the outlier tasks using a group-sparse structure. The proposed RMTL algorithm is formulated as a non-smooth convex (unconstrained) optimization problem. We propose to adopt the accelerated proximal method (APM) for solving such an optimization problem. The key component in APM is the computation of the proximal operator, which can be shown to admit an analytic solution. We also theoretically analyze the effectiveness of the RMTL algorithm. In particular, we derive a key property of the optimal solution to RMTL; moreover, based on this key property, we establish a theoretical bound for characterizing the learning performance of RMTL. Our experimental results on benchmark data sets demonstrate the effectiveness and efficiency of the proposed algorithm.
---
paper_title: A Dirty Model for Multi-task Learning

paper_content:

We consider multi-task learning in the setting of multiple linear regression, and where some relevant features could be shared across the tasks. Recent research has studied the use of l1/lq norm block-regularizations with q > 1 for such block-sparse structured problems, establishing strong guarantees on recovery even under high-dimensional scaling where the number of features scale with the number of observations. However, these papers also caution that the performance of such block-regularized methods are very dependent on the extent to which the features are shared across tasks. Indeed they show [8] that if the extent of overlap is less than a threshold, or even if parameter values in the shared features are highly uneven, then block l1/lq regularization could actually perform worse than simple separate elementwise l1 regularization. Since these caveats depend on the unknown true parameters, we might not know when and which method to apply. Even otherwise, we are far away from a realistic multi-task setting: not only do the set of relevant features have to be exactly the same across tasks, but their values have to as well. ::: ::: Here, we ask the question: can we leverage parameter overlap when it exists, but not pay a penalty when it does not? Indeed, this falls under a more general question of whether we can model such dirty data which may not fall into a single neat structural bracket (all block-sparse, or all low-rank and so on). With the explosion of such dirty high-dimensional data in modern settings, it is vital to develop tools - dirty models - to perform biased statistical estimation tailored to such data. Here, we take a first step, focusing on developing a dirty model for the multiple regression problem. Our method uses a very simple idea: we estimate a superposition of two sets of parameters and regularize them differently. We show both theoretically and empirically, our method strictly and noticeably outperforms both l1 or l1/lq methods, under high-dimensional scaling and over the entire range of possible overlaps (except at boundary cases, where we match the best method).
---
paper_title: Multi-level Lasso for Sparse Multi-task Regression

paper_content:

We present a flexible formulation for variable selection in multi-task regression to allow for discrepancies in the estimated sparsity patterns accross the multiple tasks, while leveraging the common structure among them. Our approach is based on an intuitive decomposition of the regression coe_cients into a product between a component that is common to all tasks and another component that captures task-specificity. This decomposition yields the Multi-level Lasso objective that can be solved efficiently via alternating optimization. The analysis of the "orthonormal design" case reveals some interesting insights on the nature of the shrinkage performed by our method, compared to that of related work. Theoretical guarantees are provided on the consistency of Multi-level Lasso. Simulations and empirical study of micro-array data further demonstrate the value of our framework.
---
paper_title: Spike and slab variational inference for multi-task and multiple kernel learning

paper_content:

We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi-task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multi-output Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.
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paper_title: Regularized multi--task learning

paper_content:

Past empirical work has shown that learning multiple related tasks from data simultaneously can be advantageous in terms of predictive performance relative to learning these tasks independently. In this paper we present an approach to multi--task learning based on the minimization of regularization functionals similar to existing ones, such as the one for Support Vector Machines (SVMs), that have been successfully used in the past for single--task learning. Our approach allows to model the relation between tasks in terms of a novel kernel function that uses a task--coupling parameter. We implement an instance of the proposed approach similar to SVMs and test it empirically using simulated as well as real data. The experimental results show that the proposed method performs better than existing multi--task learning methods and largely outperforms single--task learning using SVMs.
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paper_title: Learning Tree Structure in Multi-Task Learning

paper_content:

In multi-task learning (MTL), multiple related tasks are learned jointly by sharing information according to task relations. One promising approach is to utilize the given tree structure, which describes the hierarchical relations among tasks, to learn model parameters under the regularization framework. However, such a priori information is rarely available in most applications. To the best of our knowledge, there is no work to learn the tree structure among tasks and model parameters simultaneously under the regularization framework and in this paper, we develop a TAsk Tree (TAT) model for MTL to achieve this. By specifying the number of layers in the tree as H, the TAT method decomposes the parameter matrix into H component matrices, each of which corresponds to the model parameters in each layer of the tree. In order to learn the tree structure, we devise sequential constraints to make the distance between the parameters in the component matrices corresponding to each pair of tasks decrease over layers, and hence the component parameters will keep fused until the topmost layer, once they become fused in a layer. Moreover, to make the component parameters have chance to fuse in different layers, we develop a structural sparsity regularizer, which is the sum of the l2 norm on the pairwise difference among the component parameters, to learn layer-specific task structure. In order to solve the resulting non-convex objective function, we use the general iterative shrinkage and thresholding (GIST) method. By using the alternating direction method of multipliers (ADMM) method, we decompose the proximal problem in the GIST method into three independent subproblems, where a key subproblem with the sequential constraints has an efficient solution as the other two subproblems do. We also provide some theoretical analysis for the TAT model. Experiments on both synthetic and real-world datasets show the effectiveness of the TAT model.
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paper_title: A Convex Feature Learning Formulation for Latent Task Structure Discovery

paper_content:

This paper considers the multi-task learning problem and in the setting where some relevant features could be shared across few related tasks. Most of the existing methods assume the extent to which the given tasks are related or share a common feature space to be known apriori. In real-world applications however, it is desirable to automatically discover the groups of related tasks that share a feature space. In this paper we aim at searching the exponentially large space of all possible groups of tasks that may share a feature space. The main contribution is a convex formulation that employs a graph-based regularizer and simultaneously discovers few groups of related tasks, having close-by task parameters, as well as the feature space shared within each group. The regularizer encodes an important structure among the groups of tasks leading to an efficient algorithm for solving it: if there is no feature space under which a group of tasks has close-by task parameters, then there does not exist such a feature space for any of its supersets. An efficient active set algorithm that exploits this simplification and performs a clever search in the exponentially large space is presented. The algorithm is guaranteed to solve the proposed formulation (within some precision) in a time polynomial in the number of groups of related tasks discovered. Empirical results on benchmark datasets show that the proposed formulation achieves good generalization and outperforms state-of-the-art multi-task learning algorithms in some cases.
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paper_title: Hierarchical Regularization Cascade for Joint Learning

paper_content:

As the sheer volume of available benchmark datasets increases, the problem of joint learning of classifiers and knowledge-transfer between classifiers, becomes more and more relevant. We present a hierarchical approach which exploits information sharing among different classification tasks, in multitask and multi-class settings. It engages a top-down iterative method, which begins by posing an optimization problem with an incentive for large scale sharing among all classes. This incentive to share is gradually decreased, until there is no sharing and all tasks are considered separately. The method therefore exploits different levels of sharing within a given group of related tasks, without having to make hard decisions about the grouping of tasks. In order to deal with large scale problems, with many tasks and many classes, we extend our batch approach to an online setting and provide regret analysis of the algorithm. We tested our approach extensively on synthetic and real datasets, showing significant improvement over baseline and state-of-the-art methods.
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paper_title: Learning multi-level task groups in multi-task learning

paper_content:

In multi-task learning (MTL), multiple related tasks are learned jointly by sharing information across them. Many MTL algorithms have been proposed to learn the underlying task groups. However, those methods are limited to learn the task groups at only a single level, which may be not sufficient to model the complex structure among tasks in many real-world applications. In this paper, we propose a Multi-Level Task Grouping (MeTaG) method to learn the multi-level grouping structure instead of only one level among tasks. Specifically, by assuming the number of levels to be H, we decompose the parameter matrix into a sum of H component matrices, each of which is regularized with a l2 norm on the pairwise difference among parameters of all the tasks to construct level-specific task groups. For optimization, we employ the smoothing proximal gradient method to efficiently solve the objective function of the MeTaG model. Moreover, we provide theoretical analysis to show that under certain conditions the MeTaG model can recover the true parameter matrix and the true task groups in each level with high probability. We experiment our approach on both synthetic and real-world datasets, showing competitive performance over state-of-the-art MTL methods.
---
paper_title: Probabilistic Multi-Task Feature Selection

paper_content:

Recently, some variants of the l1 norm, particularly matrix norms such as the l1,2 and l1,∞ norms, have been widely used in multi-task learning, compressed sensing and other related areas to enforce sparsity via joint regularization. In this paper, we unify the l1,2 and l1,∞ norms by considering a family of l1,q norms for 1 < q < ∞ and study the problem of determining the most appropriate sparsity enforcing norm to use in the context of multi-task feature selection. Using the generalized normal distribution, we provide a probabilistic interpretation of the general multi-task feature selection problem using the l1,q norm. Based on this probabilistic interpretation, we develop a probabilistic model using the noninformative Jeffreys prior. We also extend the model to learn and exploit more general types of pairwise relationships between tasks. For both versions of the model, we devise expectation-maximization (EM) algorithms to learn all model parameters, including q, automatically. Experiments have been conducted on two cancer classification applications using microarray gene expression data.
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paper_title: Multi-domain Dialog State Tracking using Recurrent Neural Networks

paper_content:

Dialog state tracking is a key component of many modern dialog systems, most of which are designed with a single, well-defined domain in mind. This paper shows that dialog data drawn from different dialog domains can be used to train a general belief tracking model which can operate across all of these domains, exhibiting superior performance to each of the domain-specific models. We propose a training procedure which uses out-of-domain data to initialise belief tracking models for entirely new domains. This procedure leads to improvements in belief tracking performance regardless of the amount of in-domain data available for training the model.
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paper_title: Multi-task deep visual-semantic embedding for video thumbnail selection

paper_content:

Given the tremendous growth of online videos, video thumbnail, as the common visualization form of video content, is becoming increasingly important to influence user's browsing and searching experience. However, conventional methods for video thumbnail selection often fail to produce satisfying results as they ignore the side semantic information (e.g., title, description, and query) associated with the video. As a result, the selected thumbnail cannot always represent video semantics and the click-through rate is adversely affected even when the retrieved videos are relevant. In this paper, we have developed a multi-task deep visual-semantic embedding model, which can automatically select query-dependent video thumbnails according to both visual and side information. Different from most existing methods, the proposed approach employs the deep visual-semantic embedding model to directly compute the similarity between the query and video thumbnails by mapping them into a common latent semantic space, where even unseen query-thumbnail pairs can be correctly matched. In particular, we train the embedding model by exploring the large-scale and freely accessible click-through video and image data, as well as employing a multi-task learning strategy to holistically exploit the query-thumbnail relevance from these two highly related datasets. Finally, a thumbnail is selected by fusing both the representative and query relevance scores. The evaluations on 1,000 query-thumbnail dataset labeled by 191 workers in Amazon Mechanical Turk have demonstrated the effectiveness of our proposed method.
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paper_title: Cross-Stitch Networks for Multi-task Learning

paper_content:

Multi-task learning in Convolutional Networks has displayed remarkable success in the field of recognition. This success can be largely attributed to learning shared representations from multiple supervisory tasks. However, existing multi-task approaches rely on enumerating multiple network architectures specific to the tasks at hand, that do not generalize. In this paper, we propose a principled approach to learn shared representations in ConvNets using multi-task learning. Specifically, we propose a new sharing unit: "cross-stitch" unit. These units combine the activations from multiple networks and can be trained end-to-end. A network with cross-stitch units can learn an optimal combination of shared and task-specific representations. Our proposed method generalizes across multiple tasks and shows dramatically improved performance over baseline methods for categories with few training examples.
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paper_title: Deep Model Based Transfer and Multi-Task Learning for Biological Image Analysis

paper_content:

A central theme in learning from image data is to develop appropriate image representations for the specific task at hand. Traditional methods used handcrafted local features combined with high-level image representations to generate image-level representations. Thus, a practical challenge is to determine what features are appropriate for specific tasks. For example, in the study of gene expression patterns in Drosophila melanogaster, texture features based on wavelets were particularly effective for determining the developmental stages from in situ hybridization (ISH) images. Such image representation is however not suitable for controlled vocabulary (CV) term annotation because each CV term is often associated with only a part of an image. Here, we developed problem-independent feature extraction methods to generate hierarchical representations for ISH images. Our approach is based on the deep convolutional neural networks (CNNs) that can act on image pixels directly. To make the extracted features generic, the models were trained using a natural image set with millions of labeled examples. These models were transferred to the ISH image domain and used directly as feature extractors to compute image representations. Furthermore, we employed multi-task learning method to fine-tune the pre-trained models with labeled ISH images, and also extracted features from the fine-tuned models. Experimental results showed that feature representations computed by deep models based on transfer and multi-task learning significantly outperformed other methods for annotating gene expression patterns at different stage ranges. We also demonstrated that the intermediate layers of deep models produced the best gene expression pattern representations.
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paper_title: Facial Landmark Detection by Deep Multi-task Learning

paper_content:

Facial landmark detection has long been impeded by the problems of occlusion and pose variation. Instead of treating the detection task as a single and independent problem, we investigate the possibility of improving detection robustness through multi-task learning. Specifically, we wish to optimize facial landmark detection together with heterogeneous but subtly correlated tasks, e.g. head pose estimation and facial attribute inference. This is non-trivial since different tasks have different learning difficulties and convergence rates. To address this problem, we formulate a novel tasks-constrained deep model, with task-wise early stopping to facilitate learning convergence. Extensive evaluations show that the proposed task-constrained learning (i) outperforms existing methods, especially in dealing with faces with severe occlusion and pose variation, and (ii) reduces model complexity drastically compared to the state-of-the-art method based on cascaded deep model [21].
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paper_title: Heterogeneous Multi-task Learning for Human Pose Estimation with Deep Convolutional Neural Network

paper_content:

We propose an heterogeneous multi-task learning framework for human pose estimation from monocular image with deep convolutional neural network. In particular, we simultaneously learn a pose-joint regressor and a sliding-window body-part detector in a deep network architecture. We show that including the body-part detection task helps to regularize the network, directing it to converge to a good solution. We report competitive and state-of-art results on several data sets. We also empirically show that the learned neurons in the middle layer of our network are tuned to localized body parts.
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paper_title: Handling sparsity via the horseshoe

paper_content:

This paper presents a general, fully Bayesian framework for sparse supervised-learning problems based on the horseshoe prior. The horseshoe prior is a member of the family of multivariate scale mixtures of normals, and is therefore closely related to widely used approaches for sparse Bayesian learning, including, among others, Laplacian priors (e.g. the LASSO) and Student-t priors (e.g. the relevance vector machine). The advantages of the horseshoe are its robustness at handling unknown sparsity and large outlying signals. These properties are justied theoretically via a representation theorem and accompanied by comprehensive empirical experiments that compare its performance to benchmark alternatives.
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paper_title: Trace Norm Regularization: Reformulations, Algorithms, and Multi-task Learning

paper_content:

We consider a recently proposed optimization formulation of multi-task learning based on trace norm regularized least squares. While this problem may be formulated as a semidefinite program (SDP), its size is beyond general SDP solvers. Previous solution approaches apply proximal gradient methods to solve the primal problem. We derive new primal and dual reformulations of this problem, including a reduced dual formulation that involves minimizing a convex quadratic function over an operator-norm ball in matrix space. This reduced dual problem may be solved by gradient-projection methods, with each projection involving a singular value decomposition. The dual approach is compared with existing approaches and its practical effectiveness is illustrated on simulations and an application to gene expression pattern analysis.
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paper_title: Regularized multi--task learning

paper_content:

Past empirical work has shown that learning multiple related tasks from data simultaneously can be advantageous in terms of predictive performance relative to learning these tasks independently. In this paper we present an approach to multi--task learning based on the minimization of regularization functionals similar to existing ones, such as the one for Support Vector Machines (SVMs), that have been successfully used in the past for single--task learning. Our approach allows to model the relation between tasks in terms of a novel kernel function that uses a task--coupling parameter. We implement an instance of the proposed approach similar to SVMs and test it empirically using simulated as well as real data. The experimental results show that the proposed method performs better than existing multi--task learning methods and largely outperforms single--task learning using SVMs.
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paper_title: Learning Multiple Tasks with Kernel Methods

paper_content:

We study the problem of learning many related tasks simultaneously using kernel methods and regularization. The standard single-task kernel methods, such as support vector machines and regularization networks, are extended to the case of multi-task learning. Our analysis shows that the problem of estimating many task functions with regularization can be cast as a single task learning problem if a family of multi-task kernel functions we define is used. These kernels model relations among the tasks and are derived from a novel form of regularizers. Specific kernels that can be used for multi-task learning are provided and experimentally tested on two real data sets. In agreement with past empirical work on multi-task learning, the experiments show that learning multiple related tasks simultaneously using the proposed approach can significantly outperform standard single-task learning particularly when there are many related tasks but few data per task.
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paper_title: Integrating low-rank and group-sparse structures for robust multi-task learning

paper_content:

Multi-task learning (MTL) aims at improving the generalization performance by utilizing the intrinsic relationships among multiple related tasks. A key assumption in most MTL algorithms is that all tasks are related, which, however, may not be the case in many real-world applications. In this paper, we propose a robust multi-task learning (RMTL) algorithm which learns multiple tasks simultaneously as well as identifies the irrelevant (outlier) tasks. Specifically, the proposed RMTL algorithm captures the task relationships using a low-rank structure, and simultaneously identifies the outlier tasks using a group-sparse structure. The proposed RMTL algorithm is formulated as a non-smooth convex (unconstrained) optimization problem. We propose to adopt the accelerated proximal method (APM) for solving such an optimization problem. The key component in APM is the computation of the proximal operator, which can be shown to admit an analytic solution. We also theoretically analyze the effectiveness of the RMTL algorithm. In particular, we derive a key property of the optimal solution to RMTL; moreover, based on this key property, we establish a theoretical bound for characterizing the learning performance of RMTL. Our experimental results on benchmark data sets demonstrate the effectiveness and efficiency of the proposed algorithm.
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paper_title: Adaptive Multi-Task Lasso: with application to eQTL detection

paper_content:

To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects. However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared to the number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. ::: ::: In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively. Then we find the maximum a posteriori (MAP) estimation of regression coefficients and estimate weights of covariates jointly. This optimization procedure is efficient since it can be achieved by using a projected gradient descent and a coordinate descent procedure iteratively. Experimental results on simulated and real yeast datasets confirm that our model outperforms previous methods for finding eQTLs.
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paper_title: Multi-task Regression using Minimal Penalties

paper_content:

In this paper we study the kernel multiple ridge regression framework, which we refer to as multitask regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal calibration is the covariance matrix of the noise between the different tasks. We present a new algorithm to estimate this covariance matrix, based on the concept of minimal penalty, which was previously used in the single-task regression framework to estimate the variance of the noise. We show, in a non-asymptotic setting and under mild assumptions on the target function, that this estimator converges towards the covariance matrix. Then plugging this estimator into the corresponding ideal penalty leads to an oracle inequality. We illustrate the behavior of our algorithm on synthetic examples.
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paper_title: Asymmetric multi-task learning based on task relatedness and loss

paper_content:

We propose a novel multi-task learning method that minimizes the effect of negative transfer by allowing asymmetric transfer between the tasks based on task relatedness as well as the amount of individual task losses, which we refer to as Asymmetric Multi-task Learning (AMTL). To tackle this problem, we couple multiple tasks via a sparse, directed regularization graph, that enforces each task parameter to be reconstructed as a sparse combination of other tasks selected based on the task-wise loss. We present two different algorithms that jointly learn the task predictors as well as the regularization graph. The first algorithm solves for the original learning objective using alternative optimization, and the second algorithm solves an approximation of it using curriculum learning strategy, that learns one task at a time. We perform experiments on multiple datasets for classification and regression, on which we obtain significant improvements in performance over the single task learning and existing multitask learning models.
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paper_title: A Convex Formulation for Learning Task Relationships in Multi-Task Learning

paper_content:

Multi-task learning is a learning paradigm which seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this paper, we propose a regularization formulation for learning the relationships between tasks in multi-task learning. This formulation can be viewed as a novel generalization of the regularization framework for single-task learning. Besides modeling positive task correlation, our method, called multi-task relationship learning (MTRL), can also describe negative task correlation and identify outlier tasks based on the same underlying principle. Under this regularization framework, the objective function of MTRL is convex. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multi-task learning setting and then generalize it to the asymmetric setting as well. We also study the relationships between MTRL and some existing multi-task learning methods. Experiments conducted on a toy problem as well as several benchmark data sets demonstrate the effectiveness of MTRL.
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paper_title: Clustered Multi-Task Learning: A Convex Formulation

paper_content:

In multi-task learning several related tasks are considered simultaneously, with the hope that by an appropriate sharing of information across tasks, each task may benefit from the others. In the context of learning linear functions for supervised classification or regression, this can be achieved by including a priori information about the weight vectors associated with the tasks, and how they are expected to be related to each other. In this paper, we assume that tasks are clustered into groups, which are unknown beforehand, and that tasks within a group have similar weight vectors. We design a new spectral norm that encodes this a priori assumption, without the prior knowledge of the partition of tasks into groups, resulting in a new convex optimization formulation for multi-task learning. We show in simulations on synthetic examples and on the IEDB MHC-I binding dataset, that our approach outperforms well-known convex methods for multi-task learning, as well as related non-convex methods dedicated to the same problem.
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paper_title: Infinite Latent SVM for Classification and Multi-task Learning

paper_content:

Unlike existing nonparametric Bayesian models, which rely solely on specially conceived priors to incorporate domain knowledge for discovering improved latent representations, we study nonparametric Bayesian inference with regularization on the desired posterior distributions. While priors can indirectly affect posterior distributions through Bayes' theorem, imposing posterior regularization is arguably more direct and in some cases can be much easier. We particularly focus on developing infinite latent support vector machines (iLSVM) and multi-task infinite latent support vector machines (MT-iLSVM), which explore the large-margin idea in combination with a nonparametric Bayesian model for discovering predictive latent features for classification and multi-task learning, respectively. We present efficient inference methods and report empirical studies on several benchmark datasets. Our results appear to demonstrate the merits inherited from both large-margin learning and Bayesian nonparametrics.
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paper_title: Large margin multi-task metric learning

paper_content:

Multi-task learning (MTL) improves the prediction performance on multiple, different but related, learning problems through shared parameters or representations. One of the most prominent multi-task learning algorithms is an extension to support vector machines (svm) by Evgeniou et al. [15]. Although very elegant, multi-task svm is inherently restricted by the fact that support vector machines require each class to be addressed explicitly with its own weight vector which, in a multi-task setting, requires the different learning tasks to share the same set of classes. This paper proposes an alternative formulation for multi-task learning by extending the recently published large margin nearest neighbor (1mnn) algorithm to the MTL paradigm. Instead of relying on separating hyperplanes, its decision function is based on the nearest neighbor rule which inherently extends to many classes and becomes a natural fit for multi-task learning. We evaluate the resulting multi-task 1mnn on real-world insurance data and speech classification problems and show that it consistently outperforms single-task kNN under several metrics and state-of-the-art MTL classifiers.
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paper_title: A convex formulation for learning shared structures from multiple tasks

paper_content:

Multi-task learning (MTL) aims to improve generalization performance by learning multiple related tasks simultaneously. In this paper, we consider the problem of learning shared structures from multiple related tasks. We present an improved formulation (iASO) for multi-task learning based on the non-convex alternating structure optimization (ASO) algorithm, in which all tasks are related by a shared feature representation. We convert iASO, a non-convex formulation, into a relaxed convex one, which is, however, not scalable to large data sets due to its complex constraints. We propose an alternating optimization (cASO) algorithm which solves the convex relaxation efficiently, and further show that cASO converges to a global optimum. In addition, we present a theoretical condition, under which cASO can find a globally optimal solution to iASO. Experiments on several benchmark data sets confirm our theoretical analysis.
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paper_title: A Regularization Approach to Learning Task Relationships in Multitask Learning

paper_content:

Multitask learning is a learning paradigm that seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this article, we propose a regularization approach to learning the relationships between tasks in multitask learning. This approach can be viewed as a novel generalization of the regularized formulation for single-task learning. Besides modeling positive task correlation, our approach—multitask relationship learning (MTRL)—can also describe negative task correlation and identify outlier tasks based on the same underlying principle. By utilizing a matrix-variate normal distribution as a prior on the model parameters of all tasks, our MTRL method has a jointly convex objective function. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multitask learning setting and then generalize it to the asymmetric setting as well. We also discuss some variants of the regularization approach to demonstrate the use of other matrix-variate priors for learning task relationships. Moreover, to gain more insight into our model, we also study the relationships between MTRL and some existing multitask learning methods. Experiments conducted on a toy problem as well as several benchmark datasets demonstrate the effectiveness of MTRL as well as its high interpretability revealed by the task covariance matrix.
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paper_title: Flexible Clustered Multi-Task Learning by Learning Representative Tasks

paper_content:

Multi-task learning (MTL) methods have shown promising performance by learning multiple relevant tasks simultaneously, which exploits to share useful information across relevant tasks. Among various MTL methods, clustered multi-task learning (CMTL) assumes that all tasks can be clustered into groups and attempts to learn the underlying cluster structure from the training data. In this paper, we present a new approach for CMTL, called flexible clustered multi-task (FCMTL), in which the cluster structure is learned by identifying representative tasks. The new approach allows an arbitrary task to be described by multiple representative tasks, effectively soft-assigning a task to multiple clusters with different weights. Unlike existing counterpart, the proposed approach is more flexible in that (a) it does not require clusters to be disjoint, (b) tasks within one particular cluster do not have to share information to the same extent, and (c) the number of clusters is automatically inferred from data. Computationally, the proposed approach is formulated as a row-sparsity pursuit problem. We validate the proposed FCMTL on both synthetic and real-world data sets, and empirical results demonstrate that it outperforms many existing MTL methods.
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paper_title: A framework for learning predictive structures from multiple tasks and unlabeled data

paper_content:

One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting.
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paper_title: Conic Programming for Multitask Learning

paper_content:

When we have several related tasks, solving them simultaneously has been shown to be more effective than solving them individually. This approach is called multitask learning (MTL). In this paper, we propose a novel MTL algorithm. Our method controls the relatedness among the tasks locally, so all pairs of related tasks are guaranteed to have similar solutions. We apply the above idea to support vector machines and show that the optimization problem can be cast as a second-order cone program, which is convex and can be solved efficiently. The usefulness of our approach is demonstrated in ordinal regression, link prediction, and collaborative filtering, each of which can be formulated as a structured multitask problem.
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paper_title: Joint covariate selection and joint subspace selection for multiple classification problems

paper_content:

We address the problem of recovering a common set of covariates that are relevant simultaneously to several classification problems. By penalizing the sum of ? 2 norms of the blocks of coefficients associated with each covariate across different classification problems, similar sparsity patterns in all models are encouraged. To take computational advantage of the sparsity of solutions at high regularization levels, we propose a blockwise path-following scheme that approximately traces the regularization path. As the regularization coefficient decreases, the algorithm maintains and updates concurrently a growing set of covariates that are simultaneously active for all problems. We also show how to use random projections to extend this approach to the problem of joint subspace selection, where multiple predictors are found in a common low-dimensional subspace. We present theoretical results showing that this random projection approach converges to the solution yielded by trace-norm regularization. Finally, we present a variety of experimental results exploring joint covariate selection and joint subspace selection, comparing the path-following approach to competing algorithms in terms of prediction accuracy and running time.
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paper_title: Learning Sparse Task Relations in Multi-Task Learning

paper_content:

In multi-task learning, when the number of tasks is large, pairwise task relations exhibit sparse patterns since usually a task cannot be helpful to all of the other tasks and moreover, sparse task relations can reduce the risk of overfitting compared with the dense ones. In this paper, we focus on learning sparse task relations. Based on a regularization framework which can learn task relations among multiple tasks, we propose a SParse covAriance based mulTi-taSk (SPATS) model to learn a sparse covariance by using the ??? l regularization. The resulting objective function of the SPATS method is convex, which allows us to devise an alternating method to solve it. Moreover, some theoretical properties of the proposed model are studied. Experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed method.
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paper_title: Multitask learning without label correspondences

paper_content:

We propose an algorithm to perform multitask learning where each task has potentially distinct label sets and label correspondences are not readily available. This is in contrast with existing methods which either assume that the label sets shared by different tasks are the same or that there exists a label mapping oracle. Our method directly maximizes the mutual information among the labels, and we show that the resulting objective function can be efficiently optimized using existing algorithms. Our proposed approach has a direct application for data integration with different label spaces, such as integrating Yahoo! and DMOZ web directories.
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paper_title: Cross-Domain Multitask Learning with Latent Probit Models

paper_content:

Learning multiple tasks across heterogeneous domains is a challenging problem since the feature space may not be the same for different tasks. We assume the data in multiple tasks are generated from a latent common domain via sparse domain transforms and propose a latent probit model (LPM) to jointly learn the domain transforms, and a probit classifier shared in the common domain. To learn meaningful task relatedness and avoid over-fitting in classification, we introduce sparsity in the domain transforms matrices, as well as in the common classifier parameters. We derive theoretical bounds for the estimation error of the classifier parameters in terms of the sparsity of domain transform matrices. An expectation-maximization algorithm is derived for learning the LPM. The effectiveness of the approach is demonstrated on several real datasets.
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paper_title: Multilinear Multitask Learning

paper_content:

Many real world datasets occur or can be arranged into multi-modal structures. With such datasets, the tasks to be learnt can be referenced by multiple indices. Current multitask learning frameworks are not designed to account for the preservation of this information. We propose the use of multilinear algebra as a natural way to model such a set of related tasks. We present two learning methods; one is an adapted convex relaxation method used in the context of tensor completion. The second method is based on the Tucker decomposition and on alternating minimization. Experiments on synthetic and real data indicate that the multilinear approaches provide a significant improvement over other multitask learning methods. Overall our second approach yields the best performance in all datasets.
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paper_title: Geometry preserving multi-task metric learning

paper_content:

In this paper, we consider the multi-task metric learning problem, i.e., the problem of learning multiple metrics from several correlated tasks simultaneously. Despite the importance, there are only a limited number of approaches in this field. While the existing methods often straightforwardly extend existing vector-based methods, we propose to couple multiple related metric learning tasks with the von Neumann divergence. On one hand, the novel regularized approach extends previous methods from the vector regularization to a general matrix regularization framework; on the other hand and more importantly, by exploiting von Neumann divergence as the regularization, the new multi-task metric learning method has the capability to well preserve the data geometry. This leads to more appropriate propagation of side-information among tasks and provides potential for further improving the performance. We propose the concept of geometry preserving probability and show that our framework encourages a higher geometry preserving probability in theory. In addition, our formulation proves to be jointly convex and the global optimal solution can be guaranteed. We have conducted extensive experiments on six data sets (across very different disciplines), and the results verify that our proposed approach can consistently outperform almost all the current methods.
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paper_title: Multi-Task Learning in Heterogeneous Feature Spaces

paper_content:

Multi-task learning aims at improving the generalization performance of a learning task with the help of some other related tasks. Although many multi-task learning methods have been proposed, they are all based on the assumption that all tasks share the same data representation. This assumption is too restrictive for general applications. In this paper, we propose a multi-task extension of linear discriminant analysis (LDA), called multi-task discriminant analysis (MTDA), which can deal with learning tasks with different data representations. For each task, MTDA learns a separate transformation which consists of two parts, one specific to the task and one common to all tasks. A by-product of MTDA is that it can alleviate the labeled data deficiency problem of LDA. Moreover, unlike many existing multi-task learning methods, MTDA can handle binary and multi-class problems for each task in a generic way. Experimental results on face recognition show that MTDA consistently outperforms related methods.
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paper_title: Large margin multi-task metric learning

paper_content:

Multi-task learning (MTL) improves the prediction performance on multiple, different but related, learning problems through shared parameters or representations. One of the most prominent multi-task learning algorithms is an extension to support vector machines (svm) by Evgeniou et al. [15]. Although very elegant, multi-task svm is inherently restricted by the fact that support vector machines require each class to be addressed explicitly with its own weight vector which, in a multi-task setting, requires the different learning tasks to share the same set of classes. This paper proposes an alternative formulation for multi-task learning by extending the recently published large margin nearest neighbor (1mnn) algorithm to the MTL paradigm. Instead of relying on separating hyperplanes, its decision function is based on the nearest neighbor rule which inherently extends to many classes and becomes a natural fit for multi-task learning. We evaluate the resulting multi-task 1mnn on real-world insurance data and speech classification problems and show that it consistently outperforms single-task kNN under several metrics and state-of-the-art MTL classifiers.
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paper_title: Multitask learning meets tensor factorization: task imputation via convex optimization

paper_content:

We study a multitask learning problem in which each task is parametrized by a weight vector and indexed by a pair of indices, which can be e.g, (consumer, time). The weight vectors can be collected into a tensor and the (multilinear-)rank of the tensor controls the amount of sharing of information among tasks. Two types of convex relaxations have recently been proposed for the tensor multilinear rank. However, we argue that both of them are not optimal in the context of multitask learning in which the dimensions or multilinear rank are typically heterogeneous. We propose a new norm, which we call the scaled latent trace norm and analyze the excess risk of all the three norms. The results apply to various settings including matrix and tensor completion, multitask learning, and multilinear multitask learning. Both the theory and experiments support the advantage of the new norm when the tensor is not equal-sized and we do not a priori know which mode is low rank.
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paper_title: Multi-Task Learning of Gaussian Graphical Models

paper_content:

We present multi-task structure learning for Gaussian graphical models. We discuss uniqueness and boundedness of the optimal solution of the maximization problem. A block coordinate descent method leads to a provably convergent algorithm that generates a sequence of positive definite solutions. Thus, we reduce the original problem into a sequence of strictly convex l∞ regularized quadratic minimization subproblems. We further show that this subproblem leads to the continuous quadratic knapsack problem, for which very efficient methods exist. Finally we show promising results in a dataset that captures brain function of cocaine addicted and control subjects under conditions of monetary reward.
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paper_title: Learning a Kernel for Multi-Task Clustering

paper_content:

Multi-task learning has received increasing attention in the past decade. Many supervised multi-task learning methods have been proposed, while unsupervised multitask learning is still a rarely studied problem. In this paper, we propose to learn a kernel for multi-task clustering. Our goal is to learn a Reproducing Kernel Hilbert Space, in which the geometric structure of the data in each task is preserved, while the data distributions of any two tasks are as close as possible. This is formulated as a unified kernel learning framework, under which we study two types of kernel learning: nonparametric kernel learning and spectral kernel design. Both types of kernel learning can be solved by linear programming. Experiments on several cross-domain text data sets demonstrate that kernel k-means on the learned kernel can achieve better clustering results than traditional single-task clustering methods. It also outperforms the newly proposed multi-task clustering method.
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paper_title: Learning Multiple Tasks with Kernel Methods

paper_content:

We study the problem of learning many related tasks simultaneously using kernel methods and regularization. The standard single-task kernel methods, such as support vector machines and regularization networks, are extended to the case of multi-task learning. Our analysis shows that the problem of estimating many task functions with regularization can be cast as a single task learning problem if a family of multi-task kernel functions we define is used. These kernels model relations among the tasks and are derived from a novel form of regularizers. Specific kernels that can be used for multi-task learning are provided and experimentally tested on two real data sets. In agreement with past empirical work on multi-task learning, the experiments show that learning multiple related tasks simultaneously using the proposed approach can significantly outperform standard single-task learning particularly when there are many related tasks but few data per task.
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paper_title: Sparse Multi-Task Reinforcement Learning

paper_content:

In multi-task reinforcement learning (MTRL), the objective is to simultaneously learn multiple tasks and exploit their similarity to improve the performance w.r.t. single-task learning. In this paper we investigate the case when all the tasks can be accurately represented in a linear approximation space using the same small subset of the original (large) set of features. This is equivalent to assuming that the weight vectors of the task value functions are jointly sparse, i.e., the set of their non-zero components is small and it is shared across tasks. Building on existing results in multi-task regression, we develop two multi-task extensions of the fitted Q-iteration algorithm. While the first algorithm assumes that the tasks are jointly sparse in the given representation, the second one learns a transformation of the features in the attempt of finding a more sparse representation. For both algorithms we provide a sample complexity analysis and numerical simulations.
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paper_title: Smart Multitask Bregman Clustering and Multitask Kernel Clustering

paper_content:

Traditional clustering algorithms deal with a single clustering task on a single dataset. However, there are many related tasks in the real world, which motivates multitask clustering. Recently some multitask clustering algorithms have been proposed, and among them multitask Bregman clustering (MBC) is a very applicable method. MBC alternatively updates clusters and learns relationships between clusters of different tasks, and the two phases boost each other. However, the boosting does not always have positive effects on improving the clustering performance, it may also cause negative effects. Another issue of MBC is that it cannot deal with nonlinear separable data. In this article, we show that in MBC, the process of using cluster relationship to boost the cluster updating phase may cause negative effects, that is, cluster centroids may be skewed under some conditions. We propose a smart multitask Bregman clustering (S-MBC) algorithm which can identify the negative effects of the boosting and avoid the negative effects if they occur. We then propose a multitask kernel clustering (MKC) framework for nonlinear separable data by using a similar framework like MBC in the kernel space. We also propose a specific optimization method, which is quite different from that of MBC, to implement the MKC framework. Since MKC can also cause negative effects like MBC, we further extend the framework of MKC to a smart multitask kernel clustering (S-MKC) framework in a similar way that S-MBC is extended from MBC. We conduct experiments on 10 real world multitask clustering datasets to evaluate the performance of S-MBC and S-MKC. The results on clustering accuracy show that: (1) compared with the original MBC algorithm MBC, S-MBC and S-MKC perform much better; (2) compared with the convex discriminative multitask relationship clustering (DMTRC) algorithms DMTRC-L and DMTRC-R which also avoid negative transfer, S-MBC and S-MKC perform worse in the (ideal) case in which different tasks have the same cluster number and the empirical label marginal distribution in each task distributes evenly, but better or comparable in other (more general) cases. Moreover, S-MBC and S-MKC can work on the datasets in which different tasks have different number of clusters, violating the assumptions of DMTRC-L and DMTRC-R. The results on efficiency show that S-MBC and S-MKC consume more computational time than MBC and less computational time than DMTRC-L and DMTRC-R. Overall S-MBC and S-MKC are competitive compared with the state-of-the-art multitask clustering algorithms in synthetical terms of accuracy, efficiency and applicability.
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paper_title: Actor-Mimic: Deep Multitask and Transfer Reinforcement Learning

paper_content:

The ability to act in multiple environments and transfer previous knowledge to new situations can be considered a critical aspect of any intelligent agent. Towards this goal, we define a novel method of multitask and transfer learning that enables an autonomous agent to learn how to behave in multiple tasks simultaneously, and then generalize its knowledge to new domains. This method, termed "Actor-Mimic", exploits the use of deep reinforcement learning and model compression techniques to train a single policy network that learns how to act in a set of distinct tasks by using the guidance of several expert teachers. We then show that the representations learnt by the deep policy network are capable of generalizing to new tasks with no prior expert guidance, speeding up learning in novel environments. Although our method can in general be applied to a wide range of problems, we use Atari games as a testing environment to demonstrate these methods.
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paper_title: Convex Discriminative Multitask Clustering

paper_content:

Multitask clustering tries to improve the clustering performance of multiple tasks simultaneously by taking their relationship into account. Most existing multitask clustering algorithms fall into the type of generative clustering, and none are formulated as convex optimization problems. In this paper, we propose two convex Discriminative Multitask Clustering (DMTC) objectives to address the problems. The first one aims to learn a shared feature representation, which can be seen as a technical combination of the convexmultitask feature learning and the convex Multiclass Maximum Margin Clustering (M3C). The second one aims to learn the taskrelationship, which can be seen as a combination of the convex multitask relationship learning and M3C. The objectives of the two algorithms are solved in a uniform procedure by the efficient cutting-plane algorithm and further unified in the Bayesian framework. Experimental results on a toy problem and two benchmark data sets demonstrate the effectiveness of the proposed algorithms.
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paper_title: Smart multi-task Bregman clustering and multi-task kernel clustering

paper_content:

Multitask Bregman Clustering (MBC) alternatively updates clusters and learns relationship between clusters of different tasks, and the two phases boost each other. However, the boosting does not always have positive effect, it may also cause negative effect. Another issue of MBC is that it cannot deal with nonlinear separable data. In this paper, we show that MBC's process of using cluster relationship to boost the updating clusters phase may cause negative effect, i.e., cluster centroid may be skewed under some conditions. We propose a smart multi-task Bregman clustering (S-MBC) algorithm which identifies negative effect of the boosting and avoids the negative effect if it occurs.We then extend the framework of S-MBC to a smart multi-task kernel clustering (S-MKC) framework to deal with nonlinear separable data.We also propose a specific implementation of the framework which could be applied to any Mercer kernel. Experimental results confirm our analysis, and demonstrate the superiority of our proposed methods.
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paper_title: Multitask bregman clustering

paper_content:

Traditional clustering methods deal with a single clustering task on a single data set. However, in some newly emerging applications, multiple similar clustering tasks are involved simultaneously. In this case, we not only desire a partition for each task, but also want to discover the relationship among clusters of different tasks. It's also expected that the learnt relationship among tasks can improve performance of each single task. In this paper, we propose a general framework for this problem and further suggest a specific approach. In our approach, we alternatively update clusters and learn relationship between clusters of different tasks, and the two phases boost each other. Our approach is based on the general Bregman divergence, hence it's suitable for a large family of assumptions on data distributions and divergences. Empirical results on several benchmark data sets validate the approach.
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paper_title: Leveraging domain knowledge in multitask Bayesian network structure learning

paper_content:

Network structure learning algorithms have aided network discovery in fields such as bioinformatics, neuroscience, ecology and social science. However, challenges remain in learning informative networks for related sets of tasks because the search space of Bayesian network structures is characterized by large basins of approximately equivalent solutions. Multitask algorithms select a set of networks that are near each other in the search space, rather than a score-equivalent set of networks chosen from independent regions of the space. This selection preference allows a domain expert to see only differences supported by the data. However, the usefulness of these algorithms for scientific datasets is limited because existing algorithms naively assume that all pairs of tasks are equally related. We introduce a framework that relaxes this assumption by incorporating domain knowledge about task-relatedness into the learning objective. Using our framework, we introduce the first multitask Bayesian network algorithm that leverages domain knowledge about the relatedness of tasks. We use our algorithm to explore the effect of task-relatedness on network discovery and show that our algorithm learns networks that are closer to ground truth than naive algorithms and that our algorithm discovers patterns that are interesting.
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paper_title: R.: Inductive transfer for Bayesian network structure learning

paper_content:

We study the multi-task Bayesian Network structure learning problem: given data for multiple related problems, learn a Bayesian Network structure for each of them, sharing information among the problems to boost performance. We learn the structures for all the problems simultaneously using a score and search approach that encourages the learned Bayes Net structures to be similar. Encouraging similarity promotes information sharing and prioritizes learning structural features that explain the data from all problems over features that only seem relevant to a single one. This leads to a significant increase in the accuracy of the learned structures, especially when training data is scarce.
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paper_title: Multi-Task Multi-View Clustering

paper_content:

Multi-task clustering and multi-view clustering have severally found wide applications and received much attention in recent years. Nevertheless, there are many clustering problems that involve both multi-task clustering and multi-view clustering, i.e., the tasks are closely related and each task can be analyzed from multiple views. In this paper, we introduce a multi-task multi-view clustering framework which integrates within-view-task clustering, multi-view relationship learning, and multi-task relationship learning. Under this framework, we propose two multi-task multi-view clustering algorithms, the bipartite graph based multi-task multi-view clustering algorithm, and the semi-nonnegative matrix tri-factorization based multi-task multi-view clustering algorithm. The former one can deal with the multi-task multi-view clustering of nonnegative data, the latter one is a general multi-task multi-view clustering method, i.e., it can deal with the data with negative feature values. Experimental results on publicly available data sets in web page mining and image mining show the superiority of the proposed multi-task multi-view clustering algorithms over either multi-task clustering algorithms or multi-view clustering algorithms for multi-task clustering of multi-view data.
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paper_title: Multi-Task Active Learning for Linguistic Annotations

paper_content:

We extend the classical single-task active learning (AL) approach. In the multi-task active learning (MTAL) paradigm, we select examples for several annotation tasks rather than for a single one as usually done in the context of AL. We introduce two MTAL metaprotocols, alternating selection and rank combination, and propose a method to implement them in practice. We experiment with a twotask annotation scenario that includes named entity and syntactic parse tree annotations on three different corpora. MTAL outperforms random selection and a stronger baseline, onesided example selection, in which one task is pursued using AL and the selected examples are provided also to the other task.
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paper_title: Active Multi-task Learning via Bandits.

paper_content:

In multi-task learning, the multiple related tasks allow each one to benefit from the learning of the others, and labeling instances for one task can also affect the other tasks especially when the task has a small number of labeled data. Thus labeling effective instances across different learning tasks is important for improving the generalization error of all tasks. In this paper, we propose a new active multi-task learning paradigm, which selectively samples effective instances for multi-task learning. Inspired by the multi-armed bandits, which can balance the trade-off between the exploitation and exploration, we introduce a new active learning strategy and cast the selection procedure as a bandit framework. We consider both the risk of multi-task learner and the corresponding confidence bounds and our selection tries to balance this trade-off. Our proposed method is a sequential algorithm, which at each round maintains a sampling distribution on the pool of data, queries the label for an instance according to this distribution and updates the distribution based on the newly trained multi-task learner. We provide an implementation of our algorithm based on a popular multi-task learning algorithm that is trace-norm regularization method. Theoretical guarantees are developed by exploiting the Rademacher complexities. Comprehensive experiments show the effectiveness and efficiency of the proposed approach.
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paper_title: Multi-Task Learning with Labeled and Unlabeled Tasks

paper_content:

In multi-task learning, a learner is given a collection of prediction tasks and needs to solve all of them. In contrast to previous work, which required that annotated training data is available for all tasks, we consider a new setting, in which for some tasks, potentially most of them, only unlabeled training data is provided. Consequently, to solve all tasks, information must be transferred between tasks with labels and tasks without labels. Focusing on an instance-based transfer method we analyze two variants of this setting: when the set of labeled tasks is fixed, and when it can be actively selected by the learner. We state and prove a generalization bound that covers both scenarios and derive from it an algorithm for making the choice of labeled tasks (in the active case) and for transferring information between the tasks in a principled way. We also illustrate the effectiveness of the algorithm by experiments on synthetic and real data.
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paper_title: Self-adapted multi-task clustering

paper_content:

Multi-task clustering improves the clustering performance of each task by transferring knowledge across related tasks. Most existing multi-task clustering methods are based on the ideal assumption that the tasks are completely related. However, in many real applications, the tasks are usually partially related, and brute-force transfer may cause negative effect which degrades the clustering performance. In this paper, we propose a self-adapted multi-task clustering (SAMTC) method which can automatically identify and transfer reusable instances among the tasks, thus avoiding negative transfer. SAMTC begins with an initialization by performing single-task clustering on each task, then executes the following three steps: first, it finds the reusable instances by measuring related clusters with Jensen-Shannon divergence between each pair of tasks, and obtains a pair of possibly related subtasks; second, it estimates the relatedness between each pair of subtasks with kernel mean matching; third, it constructs the similarity matrix for each task by exploiting useful information from the other tasks through instance transfer, and adopts spectral clustering to get the final clustering result. Experimental results on several real data sets show the superiority of the proposed algorithm over traditional single-task clustering methods and existing multitask clustering methods.
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paper_title: Semisupervised Multitask Learning

paper_content:

Context plays an important role when performing classification, and in this paper we examine context from two perspectives. First, the classification of items within a single task is placed within the context of distinct concurrent or previous classification tasks (multiple distinct data collections). This is referred to as multi-task learning (MTL), and is implemented here in a statistical manner, using a simplified form of the Dirichlet process. In addition, when performing many classification tasks one has simultaneous access to all unlabeled data that must be classified, and therefore there is an opportunity to place the classification of any one feature vector within the context of all unlabeled feature vectors; this is referred to as semi-supervised learning. In this paper we integrate MTL and semi-supervised learning into a single framework, thereby exploiting two forms of contextual information. Example results are presented on a "toy" example, to demonstrate the concept, and the algorithm is also applied to three real data sets.
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paper_title: Multi-task reinforcement learning: a hierarchical Bayesian approach

paper_content:

We consider the problem of multi-task reinforcement learning, where the agent needs to solve a sequence of Markov Decision Processes (MDPs) chosen randomly from a fixed but unknown distribution. We model the distribution over MDPs using a hierarchical Bayesian infinite mixture model. For each novel MDP, we use the previously learned distribution as an informed prior for modelbased Bayesian reinforcement learning. The hierarchical Bayesian framework provides a strong prior that allows us to rapidly infer the characteristics of new environments based on previous environments, while the use of a nonparametric model allows us to quickly adapt to environments we have not encountered before. In addition, the use of infinite mixtures allows for the model to automatically learn the number of underlying MDP components. We evaluate our approach and show that it leads to significant speedups in convergence to an optimal policy after observing only a small number of tasks.
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paper_title: Semi-Supervised Multitask Learning

paper_content:

A semi-supervised multitask learning (MTL) framework is presented, in which M parameterized semi-supervised classifiers, each associated with one of M partially labeled data manifolds, are learned jointly under the constraint of a soft-sharing prior imposed over the parameters of the classifiers. The unlabeled data are utilized by basing classifier learning on neighborhoods, induced by a Markov random walk over a graph representation of each manifold. Experimental results on real data sets demonstrate that semi-supervised MTL yields significant improvements in generalization performance over either semi-supervised single-task learning (STL) or supervised MTL.
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paper_title: Semi-Supervised Multi-Task Regression

paper_content:

Labeled data are needed for many machine learning applications but the amount available in some applications is scarce. Semi-supervised learning and multi-task learning are two of the approaches that have been proposed to alleviate this problem. In this paper, we seek to integrate these two approaches for regression applications. We first propose a new supervised multi-task regression method called SMTR, which is based on Gaussian processes (GP) with the assumption that the kernel parameters for all tasks share a common prior. We then incorporate unlabeled data into SMTR by changing the kernel function of the GP prior to a data-dependent kernel function, resulting in a semi-supervised extension of SMTR, called SSMTR. Moreover, we incorporate pairwise information into SSMTR to further boost the learning performance for applications in which such information is available. Experiments conducted on two commonly used data sets for multi-task regression demonstrate the effectiveness of our methods.
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paper_title: Inductive multi-task learning with multiple view data

paper_content:

In many real-world applications, it is becoming common to have data extracted from multiple diverse sources, known as "multi-view" data. Multi-view learning (MVL) has been widely studied in many applications, but existing MVL methods learn a single task individually. In this paper, we study a new direction of multi-view learning where there are multiple related tasks with multi-view data (i.e. multi-view multi-task learning, or MVMT Learning). In our MVMT learning methods, we learn a linear mapping for each view in each task. In a single task, we use co-regularization to obtain functions that are in-agreement with each other on the unlabeled samples and achieve low classification errors on the labeled samples simultaneously. Cross different tasks, additional regularization functions are utilized to ensure the functions that we learn in each view are similar. We also developed two extensions of the MVMT learning algorithm. One extension handles missing views and the other handles non-uniformly related tasks. Experimental studies on three real-world data sets demonstrate that our MVMT methods significantly outperform the existing state-of-the-art methods.
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paper_title: Bayesian Multi-Task Reinforcement Learning

paper_content:

We consider the problem of multi-task reinforcement learning where the learner is provided with a set of tasks, for which only a small number of samples can be generated for any given policy. As the number of samples may not be enough to learn an accurate evaluation of the policy, it would be necessary to identify classes of tasks with similar structure and to learn them jointly. We consider the case where the tasks share structure in their value functions, and model this by assuming that the value functions are all sampled from a common prior. We adopt the Gaussian process temporal-difference value function model and use a hierarchical Bayesian approach to model the distribution over the value functions. We study two cases, where all the value functions belong to the same class and where they belong to an undefined number of classes. For each case, we present a hierarchical Bayesian model, and derive inference algorithms for (i) joint learning of the value functions, and (ii) efficient transfer of the information gained in (i) to assist learning the value function of a newly observed task.
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paper_title: Bayesian Online Multitask Learning of Gaussian Processes

paper_content:

Standard single-task kernel methods have recently been extended to the case of multitask learning in the context of regularization theory. There are experimental results, especially in biomedicine, showing the benefit of the multitask approach compared to the single-task one. However, a possible drawback is computational complexity. For instance, when regularization networks are used, complexity scales as the cube of the overall number of training data, which may be large when several tasks are involved. The aim of this paper is to derive an efficient computational scheme for an important class of multitask kernels. More precisely, a quadratic loss is assumed and each task consists of the sum of a common term and a task-specific one. Within a Bayesian setting, a recursive online algorithm is obtained, which updates both estimates and confidence intervals as new data become available. The algorithm is tested on two simulated problems and a real data set relative to xenobiotics administration in human patients.
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paper_title: Online Multi-task Learning with Hard Constraints

paper_content:

We discuss multi-task online learning when a decision maker has to deal simultaneously with M tasks. The tasks are related, which is modeled by imposing that the M-tuple of actions taken by the decision maker needs to satisfy certain constraints. We give natural examples of such restrictions and then discuss a general class of tractable constraints, for which we introduce computationally efficient ways of selecting actions, essentially by reducing to an on-line shortest path problem. We briefly discuss "tracking" and "bandit" versions of the problem and extend the model in various ways, including non-additive global losses and uncountably infinite sets of tasks.
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paper_title: Online learning of multiple tasks with a shared loss

paper_content:

We study the problem of learning multiple tasks in parallel within the online learning framework. On each online round, the algorithm receives an instance for each of the parallel tasks and responds by predicting the label of each instance. We consider the case where the predictions made on each round all contribute toward a common goal. The relationship between the various tasks is defined by a global loss function, which evaluates the overall quality of the multiple predictions made on each round. Specifically, each individual prediction is associated with its own loss value, and then these multiple loss values are combined into a single number using the global loss function. We focus on the case where the global loss function belongs to the family of absolute norms, and present several online learning algorithms for the induced problem. We prove worst-case relative loss bounds for all of our algorithms, and demonstrate the effectiveness of our approach on a large-scale multiclass-multilabel text categorization problem.
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paper_title: Feature hashing for large scale multitask learning

paper_content:

Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction between random subspaces is negligible with high probability. We demonstrate the feasibility of this approach with experimental results for a new use case --- multitask learning with hundreds of thousands of tasks.
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paper_title: Linear Algorithms for Online Multitask Classification

paper_content:

Stainless steel articles such as support pins for color television tube shadow mask assemblies are rendered resistant to the formation of surface nodules promoting tube breakage by processing through a vacuum-firing heat treatment prior to use.
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paper_title: Multi-Task Learning in Heterogeneous Feature Spaces

paper_content:

Multi-task learning aims at improving the generalization performance of a learning task with the help of some other related tasks. Although many multi-task learning methods have been proposed, they are all based on the assumption that all tasks share the same data representation. This assumption is too restrictive for general applications. In this paper, we propose a multi-task extension of linear discriminant analysis (LDA), called multi-task discriminant analysis (MTDA), which can deal with learning tasks with different data representations. For each task, MTDA learns a separate transformation which consists of two parts, one specific to the task and one common to all tasks. A by-product of MTDA is that it can alleviate the labeled data deficiency problem of LDA. Moreover, unlike many existing multi-task learning methods, MTDA can handle binary and multi-class problems for each task in a generic way. Experimental results on face recognition show that MTDA consistently outperforms related methods.
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paper_title: Parallel Multi-task Learning

paper_content:

In this paper, we develop parallel algorithms for a family of regularized multi-task methods which can model task relations under the regularization framework. Since those multi-task methods cannot be parallelized directly, we use the FISTA algorithm, which in each iteration constructs a surrogate function of the original problem by utilizing the Lipschitz structure of the objective function based on the solution in the last iteration, to solve it. Specifically, we investigate the dual form of the objective function in those methods by adopting the hinge, e-insensitive, and square losses to deal with multi-task classification and regression problems, and then utilize the Lipschitz structure to construct the surrogate function for the dual forms. The surrogate functions constructed in the FISTA algorithm are founded to be decomposable, leading to parallel designs for those multi-task methods. Experiments on several benchmark datasets show that the convergence of the proposed algorithms is as fast as that of SMO-style algorithms and the parallel design can speedup the computation.
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paper_title: Online Multitask Learning

paper_content:

We study the problem of online learning of multiple tasks in parallel. On each online round, the algorithm receives an instance and makes a prediction for each one of the parallel tasks. We consider the case where these tasks all contribute toward a common goal. We capture the relationship between the tasks by using a single global loss function to evaluate the quality of the multiple predictions made on each round. Specifically, each individual prediction is associated with its own individual loss, and then these loss values are combined using a global loss function. We present several families of online algorithms which can use any absolute norm as a global loss function. We prove worst-case relative loss bounds for all of our algorithms.
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paper_title: Distributed Multi-Task Learning

paper_content:

We consider the problem of distributed multitask learning, where each machine learns a separate, but related, task. Specifically, each machine learns a linear predictor in high-dimensional space, where all tasks share the same small support. We present a communication-efficient estimator based on the debiased lasso and show that it is comparable with the optimal centralized method.
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paper_title: Online Learning of Multiple Tasks and Their Relationships

paper_content:

We propose an Online MultiTask Learning (Omtl) framework which simultaneously learns the task weight vectors as well as the task relatedness adaptively from the data. Our work is in contrast with prior work on online multitask learning which assumes fixed task relatedness, a priori. Furthermore, whereas prior work in such settings assume only positively correlated tasks, our framework can capture negative correlations as well. Our proposed framework learns the task relationship matrix by framing the objective function as a Bregman divergence minimization problem for positive definite matrices. Subsequently, we exploit this adaptively learned task-relationship matrix to select the most informative samples in an online multitask active learning setting. Experimental results on a number of real-world datasets and comparisons with numerous baselines establish the efficacy of our proposed approach.
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paper_title: A framework for learning predictive structures from multiple tasks and unlabeled data

paper_content:

One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting.
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paper_title: Robust Visual Tracking via Structured Multi-Task Sparse Learning

paper_content:

In this paper, we formulate object tracking in a particle filter framework as a structured multi-task sparse learning problem, which we denote as Structured Multi-Task Tracking (S-MTT). Since we model particles as linear combinations of dictionary templates that are updated dynamically, learning the representation of each particle is considered a single task in Multi-Task Tracking (MTT). By employing popular sparsity-inducing $$\ell _{p,q}$$ mixed norms $$(\text{ specifically} p\in \{2,\infty \}$$ and $$q=1),$$ we regularize the representation problem to enforce joint sparsity and learn the particle representations together. As compared to previous methods that handle particles independently, our results demonstrate that mining the interdependencies between particles improves tracking performance and overall computational complexity. Interestingly, we show that the popular $$L_1$$ tracker (Mei and Ling, IEEE Trans Pattern Anal Mach Intel 33(11):2259---2272, 2011) is a special case of our MTT formulation (denoted as the $$L_{11}$$ tracker) when $$p=q=1.$$ Under the MTT framework, some of the tasks (particle representations) are often more closely related and more likely to share common relevant covariates than other tasks. Therefore, we extend the MTT framework to take into account pairwise structural correlations between particles (e.g. spatial smoothness of representation) and denote the novel framework as S-MTT. The problem of learning the regularized sparse representation in MTT and S-MTT can be solved efficiently using an Accelerated Proximal Gradient (APG) method that yields a sequence of closed form updates. As such, S-MTT and MTT are computationally attractive. We test our proposed approach on challenging sequences involving heavy occlusion, drastic illumination changes, and large pose variations. Experimental results show that S-MTT is much better than MTT, and both methods consistently outperform state-of-the-art trackers.
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paper_title: Scalable Multitask Representation Learning for Scene Classification

paper_content:

The underlying idea of multitask learning is that learning tasks jointly is better than learning each task individually. In particular, if only a few training examples are available for each task, sharing a jointly trained representation improves classification performance. In this paper, we propose a novel multitask learning method that learns a low-dimensional representation jointly with the corresponding classifiers, which are then able to profit from the latent inter-class correlations. Our method scales with respect to the original feature dimension and can be used with high-dimensional image descriptors such as the Fisher Vector. Furthermore, it consistently outperforms the current state of the art on the SUN397 scene classification benchmark with varying amounts of training data.
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paper_title: Robust visual tracking via multi-task sparse learning

paper_content:

In this paper, we formulate object tracking in a particle filter framework as a multi-task sparse learning problem, which we denote as Multi-Task Tracking (MTT). Since we model particles as linear combinations of dictionary templates that are updated dynamically, learning the representation of each particle is considered a single task in MTT. By employing popular sparsity-inducing l p, q mixed norms (p Є {2, ∞} and q = 1), we regularize the representation problem to enforce joint sparsity and learn the particle representations together. As compared to previous methods that handle particles independently, our results demonstrate that mining the interdependencies between particles improves tracking performance and overall computational complexity. Interestingly, we show that the popular L 1 tracker [15] is a special case of our MTT formulation (denoted as the L 11 tracker) when p = q = 1. The learning problem can be efficiently solved using an Accelerated Proximal Gradient (APG) method that yields a sequence of closed form updates. As such, MTT is computationally attractive. We test our proposed approach on challenging sequences involving heavy occlusion, drastic illumination changes, and large pose variations. Experimental results show that MTT methods consistently outperform state-of-the-art trackers.
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paper_title: Learning to Transfer: Transferring Latent Task Structures and Its Application to Person-Specific Facial Action Unit Detection

paper_content:

In this article we explore the problem of constructing person-specific models for the detection of facial Action Units (AUs), addressing the problem from the point of view of Transfer Learning and Multi-Task Learning. Our starting point is the fact that some expressions, such as smiles, are very easily elicited, annotated, and automatically detected, while others are much harder to elicit and to annotate. We thus consider a novel problem: all AU models for the target subject are to be learnt using person-specific annotated data for a reference AU (AU12 in our case), and no data or little data regarding the target AU. In order to design such a model, we propose a novel Multi-Task Learning and the associated Transfer Learning framework, in which we consider both relations across subjects and AUs. That is to say, we consider a tensor structure among the tasks. Our approach hinges on learning the latent relations among tasks using one single reference AU, and then transferring these latent relations to other AUs. We show that we are able to effectively make use of the annotated data for AU12 when learning other person-specific AU models, even in the absence of data for the target task. Finally, we show the excellent performance of our method when small amounts of annotated data for the target tasks are made available.
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paper_title: No Matter Where You Are: Flexible Graph-Guided Multi-task Learning for Multi-view Head Pose Classification under Target Motion

paper_content:

We propose a novel Multi-Task Learning framework (FEGA-MTL) for classifying the head pose of a person who moves freely in an environment monitored by multiple, large field-of-view surveillance cameras. As the target (person) moves, distortions in facial appearance owing to camera perspective and scale severely impede performance of traditional head pose classification methods. FEGA-MTL operates on a dense uniform spatial grid and learns appearance relationships across partitions as well as partition-specific appearance variations for a given head pose to build region-specific classifiers. Guided by two graphs which a-priori model appearance similarity among (i) grid partitions based on camera geometry and (ii) head pose classes, the learner efficiently clusters appearance wise related grid partitions to derive the optimal partitioning. For pose classification, upon determining the target's position using a person tracker, the appropriate region specific classifier is invoked. Experiments confirm that FEGA-MTL achieves state-of-the-art classification with few training data.
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paper_title: Multi-Task Learning with Low Rank Attribute Embedding for Person Re-Identification

paper_content:

We propose a novel Multi-Task Learning with Low Rank Attribute Embedding (MTL-LORAE) framework for person re-identification. Re-identifications from multiple cameras are regarded as related tasks to exploit shared information to improve re-identification accuracy. Both low level features and semantic/data-driven attributes are utilized. Since attributes are generally correlated, we introduce a low rank attribute embedding into the MTL formulation to embed original binary attributes to a continuous attribute space, where incorrect and incomplete attributes are rectified and recovered to better describe people. The learning objective function consists of a quadratic loss regarding class labels and an attribute embedding error, which is solved by an alternating optimization procedure. Experiments on three person re-identification datasets have demonstrated that MTL-LORAE outperforms existing approaches by a large margin and produces state-of-the-art results.
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paper_title: Sparse multi-task regression and feature selection to identify brain imaging predictors for memory performance

paper_content:

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by progressive impairment of memory and other cognitive functions, which makes regression analysis a suitable model to study whether neuroimaging measures can help predict memory performance and track the progression of AD. Existing memory performance prediction methods via regression, however, do not take into account either the interconnected structures within imaging data or those among memory scores, which inevitably restricts their predictive capabilities. To bridge this gap, we propose a novel Sparse Multi-tAsk Regression and feaTure selection (SMART) method to jointly analyze all the imaging and clinical data under a single regression framework and with shared underlying sparse representations. Two convex regularizations are combined and used in the model to enable sparsity as well as facilitate multi-task learning. The effectiveness of the proposed method is demonstrated by both clearly improved prediction performances in all empirical test cases and a compact set of selected RAVLT-relevant MRI predictors that accord with prior studies.
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paper_title: Multi-task deep visual-semantic embedding for video thumbnail selection

paper_content:

Given the tremendous growth of online videos, video thumbnail, as the common visualization form of video content, is becoming increasingly important to influence user's browsing and searching experience. However, conventional methods for video thumbnail selection often fail to produce satisfying results as they ignore the side semantic information (e.g., title, description, and query) associated with the video. As a result, the selected thumbnail cannot always represent video semantics and the click-through rate is adversely affected even when the retrieved videos are relevant. In this paper, we have developed a multi-task deep visual-semantic embedding model, which can automatically select query-dependent video thumbnails according to both visual and side information. Different from most existing methods, the proposed approach employs the deep visual-semantic embedding model to directly compute the similarity between the query and video thumbnails by mapping them into a common latent semantic space, where even unseen query-thumbnail pairs can be correctly matched. In particular, we train the embedding model by exploring the large-scale and freely accessible click-through video and image data, as well as employing a multi-task learning strategy to holistically exploit the query-thumbnail relevance from these two highly related datasets. Finally, a thumbnail is selected by fusing both the representative and query relevance scores. The evaluations on 1,000 query-thumbnail dataset labeled by 191 workers in Amazon Mechanical Turk have demonstrated the effectiveness of our proposed method.
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paper_title: Multi-task CNN Model for Attribute Prediction

paper_content:

This paper proposes a joint multi-task learning algorithm to better predict attributes in images using deep convolutional neural networks (CNN). We consider learning binary semantic attributes through a multi-task CNN model, where each CNN will predict one binary attribute. The multi-task learning allows CNN models to simultaneously share visual knowledge among different attribute categories. Each CNN will generate attribute-specific feature representations, and then we apply multi-task learning on the features to predict their attributes. In our multi-task framework, we propose a method to decompose the overall model’s parameters into a latent task matrix and combination matrix. Furthermore, under-sampled classifiers can leverage shared statistics from other classifiers to improve their performance. Natural grouping of attributes is applied such that attributes in the same group are encouraged to share more knowledge. Meanwhile, attributes in different groups will generally compete with each other, and consequently share less knowledge. We show the effectiveness of our method on two popular attribute datasets.
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paper_title: Multi-task warped Gaussian process for personalized age estimation

paper_content:

Automatic age estimation from facial images has aroused research interests in recent years due to its promising potential for some computer vision applications. Among the methods proposed to date, personalized age estimation methods generally outperform global age estimation methods by learning a separate age estimator for each person in the training data set. However, since typical age databases only contain very limited training data for each person, training a separate age estimator using only training data for that person runs a high risk of overfitting the data and hence the prediction performance is limited. In this paper, we propose a novel approach to age estimation by formulating the problem as a multi-task learning problem. Based on a variant of the Gaussian process (GP) called warped Gaussian process (WGP), we propose a multi-task extension called multi-task warped Gaussian process (MTWGP). Age estimation is formulated as a multi-task regression problem in which each learning task refers to estimation of the age function for each person. While MTWGP models common features shared by different tasks (persons), it also allows task-specific (person-specific) features to be learned automatically. Moreover, unlike previous age estimation methods which need to specify the form of the regression functions or determine many parameters in the functions using inefficient methods such as cross validation, the form of the regression functions in MTWGP is implicitly defined by the kernel function and all its model parameters can be learned from data automatically. We have conducted experiments on two publicly available age databases, FG-NET and MORPH. The experimental results are very promising in showing that MTWGP compares favorably with state-of-the-art age estimation methods.
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paper_title: Multilinear Multitask Learning

paper_content:

Many real world datasets occur or can be arranged into multi-modal structures. With such datasets, the tasks to be learnt can be referenced by multiple indices. Current multitask learning frameworks are not designed to account for the preservation of this information. We propose the use of multilinear algebra as a natural way to model such a set of related tasks. We present two learning methods; one is an adapted convex relaxation method used in the context of tensor completion. The second method is based on the Tucker decomposition and on alternating minimization. Experiments on synthetic and real data indicate that the multilinear approaches provide a significant improvement over other multitask learning methods. Overall our second approach yields the best performance in all datasets.
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paper_title: A Dirty Model for Multi-task Learning

paper_content:

We consider multi-task learning in the setting of multiple linear regression, and where some relevant features could be shared across the tasks. Recent research has studied the use of l1/lq norm block-regularizations with q > 1 for such block-sparse structured problems, establishing strong guarantees on recovery even under high-dimensional scaling where the number of features scale with the number of observations. However, these papers also caution that the performance of such block-regularized methods are very dependent on the extent to which the features are shared across tasks. Indeed they show [8] that if the extent of overlap is less than a threshold, or even if parameter values in the shared features are highly uneven, then block l1/lq regularization could actually perform worse than simple separate elementwise l1 regularization. Since these caveats depend on the unknown true parameters, we might not know when and which method to apply. Even otherwise, we are far away from a realistic multi-task setting: not only do the set of relevant features have to be exactly the same across tasks, but their values have to as well. ::: ::: Here, we ask the question: can we leverage parameter overlap when it exists, but not pay a penalty when it does not? Indeed, this falls under a more general question of whether we can model such dirty data which may not fall into a single neat structural bracket (all block-sparse, or all low-rank and so on). With the explosion of such dirty high-dimensional data in modern settings, it is vital to develop tools - dirty models - to perform biased statistical estimation tailored to such data. Here, we take a first step, focusing on developing a dirty model for the multiple regression problem. Our method uses a very simple idea: we estimate a superposition of two sets of parameters and regularize them differently. We show both theoretically and empirically, our method strictly and noticeably outperforms both l1 or l1/lq methods, under high-dimensional scaling and over the entire range of possible overlaps (except at boundary cases, where we match the best method).
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paper_title: Rotating your face using multi-task deep neural network

paper_content:

Face recognition under viewpoint and illumination changes is a difficult problem, so many researchers have tried to solve this problem by producing the pose- and illumination- invariant feature. Zhu et al. [26] changed all arbitrary pose and illumination images to the frontal view image to use for the invariant feature. In this scheme, preserving identity while rotating pose image is a crucial issue. This paper proposes a new deep architecture based on a novel type of multitask learning, which can achieve superior performance in rotating to a target-pose face image from an arbitrary pose and illumination image while preserving identity. The target pose can be controlled by the user's intention. This novel type of multi-task model significantly improves identity preservation over the single task model. By using all the synthesized controlled pose images, called Controlled Pose Image (CPI), for the pose-illumination-invariant feature and voting among the multiple face recognition results, we clearly outperform the state-of-the-art algorithms by more than 4∼6% on the MultiPIE dataset.
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paper_title: Hierarchical kernel stick-breaking process for multi-task image analysis

paper_content:

The kernel stick-breaking process (KSBP) is employed to segment general imagery, imposing the condition that patches (small blocks of pixels) that are spatially proximate are more likely to be associated with the same cluster (segment). The number of clusters is not set a priori and is inferred from the hierarchical Bayesian model. Further, KSBP is integrated with a shared Dirichlet process prior to simultaneously model multiple images, inferring their inter-relationships. This latter application may be useful for sorting and learning relationships between multiple images. The Bayesian inference algorithm is based on a hybrid of variational Bayesian analysis and local sampling. In addition to providing details on the model and associated inference framework, example results are presented for several image-analysis problems.
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paper_title: Boosted multi-task learning for face verification with applications to web image and video search

paper_content:

Face verification has many potential applications including filtering and ranking image/video search results on celebrities. Since these images/videos are taken under uncontrolled environments, the problem is very challenging due to dramatic lighting and pose variations, low resolutions, compression artifacts, etc. In addition, the available number of training images for each celebrity may be limited, hence learning individual classifiers for each person may cause overfitting. In this paper, we propose two ideas to meet the above challenges. First, we propose to use individual bins, instead of whole histograms, of Local Binary Patterns (LBP) as features for learning, which yields significant performance improvements and computation reduction in our experiments. Second, we present a novel Multi-Task Learning (MTL) framework, called Boosted MTL, for face verification with limited training data. It jointly learns classifiers for multiple people by sharing a few boosting classifiers in order to avoid overfitting. The effectiveness of Boosted MTL and LBP bin features is verified with a large number of celebrity images/videos from the web.
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paper_title: Saliency Detection by Multitask Sparsity Pursuit

paper_content:

This paper addresses the problem of detecting salient areas within natural images. We shall mainly study the problem under unsupervised setting, i.e., saliency detection without learning from labeled images. A solution of multitask sparsity pursuit is proposed to integrate multiple types of features for detecting saliency collaboratively. Given an image described by multiple features, its saliency map is inferred by seeking the consistently sparse elements from the joint decompositions of multiple-feature matrices into pairs of low-rank and sparse matrices. The inference process is formulated as a constrained nuclear norm and as an l2,1 -norm minimization problem, which is convex and can be solved efficiently with an augmented Lagrange multiplier method. Compared with previous methods, which usually make use of multiple features by combining the saliency maps obtained from individual features, the proposed method seamlessly integrates multiple features to produce jointly the saliency map with a single inference step and thus produces more accurate and reliable results. In addition to the unsupervised setting, the proposed method can be also generalized to incorporate the top-down priors obtained from supervised environment. Extensive experiments well validate its superiority over other state-of-the-art methods.
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paper_title: Facial Landmark Detection by Deep Multi-task Learning

paper_content:

Facial landmark detection has long been impeded by the problems of occlusion and pose variation. Instead of treating the detection task as a single and independent problem, we investigate the possibility of improving detection robustness through multi-task learning. Specifically, we wish to optimize facial landmark detection together with heterogeneous but subtly correlated tasks, e.g. head pose estimation and facial attribute inference. This is non-trivial since different tasks have different learning difficulties and convergence rates. To address this problem, we formulate a novel tasks-constrained deep model, with task-wise early stopping to facilitate learning convergence. Extensive evaluations show that the proposed task-constrained learning (i) outperforms existing methods, especially in dealing with faces with severe occlusion and pose variation, and (ii) reduces model complexity drastically compared to the state-of-the-art method based on cascaded deep model [21].
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paper_title: Multi-task Sparse Learning with Beta Process Prior for Action Recognition

paper_content:

In this paper, we formulate human action recognition as a novel Multi-Task Sparse Learning(MTSL) framework which aims to construct a test sample with multiple features from as few bases as possible. Learning the sparse representation under each feature modality is considered as a single task in MTSL. Since the tasks are generated from multiple features associated with the same visual input, they are not independent but inter-related. We introduce a Beta process(BP) prior to the hierarchical MTSL model, which efficiently learns a compact dictionary and infers the sparse structure shared across all the tasks. The MTSL model enforces the robustness in coefficient estimation compared with performing each task independently. Besides, the sparseness is achieved via the Beta process formulation rather than the computationally expensive L1 norm penalty. In terms of non-informative gamma hyper-priors, the sparsity level is totally decided by the data. Finally, the learning problem is solved by Gibbs sampling inference which estimates the full posterior on the model parameters. Experimental results on the KTH and UCF sports datasets demonstrate the effectiveness of the proposed MTSL approach for action recognition.
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paper_title: Visual classification with multi-task joint sparse representation

paper_content:

We address the problem of computing joint sparse representation of visual signal across multiple kernel-based representations. Such a problem arises naturally in supervised visual recognition applications where one aims to reconstruct a test sample with multiple features from as few training subjects as possible. We cast the linear version of this problem into a multi-task joint covariate selection model [15], which can be very efficiently optimized via ker-nelizable accelerated proximal gradient method. Furthermore, two kernel-view extensions of this method are provided to handle the situations where descriptors and similarity functions are in the form of kernel matrices. We then investigate into two applications of our algorithm to feature combination: 1) fusing gray-level and LBP features for face recognition, and 2) combining multiple kernels for object categorization. Experimental results on challenging real-world datasets show that the feature combination capability of our proposed algorithm is competitive to the state-of-the-art multiple kernel learning methods.
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paper_title: Multi-task Recurrent Neural Network for Immediacy Prediction

paper_content:

In this paper, we propose to predict immediacy for interacting persons from still images. A complete immediacy set includes interactions, relative distance, body leaning direction and standing orientation. These measures are found to be related to the attitude, social relationship, social interaction, action, nationality, and religion of the communicators. A large-scale dataset with 10,000 images is constructed, in which all the immediacy measures and the human poses are annotated. We propose a rich set of immediacy representations that help to predict immediacy from imperfect 1-person and 2-person pose estimation results. A multi-task deep recurrent neural network is constructed to take the proposed rich immediacy representation as input and learn the complex relationship among immediacy predictions multiple steps of refinement. The effectiveness of the proposed approach is proved through extensive experiments on the large scale dataset.
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paper_title: Multitask learning meets tensor factorization: task imputation via convex optimization

paper_content:

We study a multitask learning problem in which each task is parametrized by a weight vector and indexed by a pair of indices, which can be e.g, (consumer, time). The weight vectors can be collected into a tensor and the (multilinear-)rank of the tensor controls the amount of sharing of information among tasks. Two types of convex relaxations have recently been proposed for the tensor multilinear rank. However, we argue that both of them are not optimal in the context of multitask learning in which the dimensions or multilinear rank are typically heterogeneous. We propose a new norm, which we call the scaled latent trace norm and analyze the excess risk of all the three norms. The results apply to various settings including matrix and tensor completion, multitask learning, and multilinear multitask learning. Both the theory and experiments support the advantage of the new norm when the tensor is not equal-sized and we do not a priori know which mode is low rank.
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paper_title: Tracking via Robust Multi-task Multi-view Joint Sparse Representation

paper_content:

Combining multiple observation views has proven beneficial for tracking. In this paper, we cast tracking as a novel multi-task multi-view sparse learning problem and exploit the cues from multiple views including various types of visual features, such as intensity, color, and edge, where each feature observation can be sparsely represented by a linear combination of atoms from an adaptive feature dictionary. The proposed method is integrated in a particle filter framework where every view in each particle is regarded as an individual task. We jointly consider the underlying relationship between tasks across different views and different particles, and tackle it in a unified robust multi-task formulation. In addition, to capture the frequently emerging outlier tasks, we decompose the representation matrix to two collaborative components which enable a more robust and accurate approximation. We show that the proposed formulation can be efficiently solved using the Accelerated Proximal Gradient method with a small number of closed-form updates. The presented tracker is implemented using four types of features and is tested on numerous benchmark video sequences. Both the qualitative and quantitative results demonstrate the superior performance of the proposed approach compared to several state-of-the-art trackers.
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paper_title: Heterogeneous Multi-task Learning for Human Pose Estimation with Deep Convolutional Neural Network

paper_content:

We propose an heterogeneous multi-task learning framework for human pose estimation from monocular image with deep convolutional neural network. In particular, we simultaneously learn a pose-joint regressor and a sliding-window body-part detector in a deep network architecture. We show that including the body-part detection task helps to regularize the network, directing it to converge to a good solution. We report competitive and state-of-art results on several data sets. We also empirically show that the learned neurons in the middle layer of our network are tuned to localized body parts.
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paper_title: Regularized multi--task learning

paper_content:

Past empirical work has shown that learning multiple related tasks from data simultaneously can be advantageous in terms of predictive performance relative to learning these tasks independently. In this paper we present an approach to multi--task learning based on the minimization of regularization functionals similar to existing ones, such as the one for Support Vector Machines (SVMs), that have been successfully used in the past for single--task learning. Our approach allows to model the relation between tasks in terms of a novel kernel function that uses a task--coupling parameter. We implement an instance of the proposed approach similar to SVMs and test it empirically using simulated as well as real data. The experimental results show that the proposed method performs better than existing multi--task learning methods and largely outperforms single--task learning using SVMs.
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paper_title: Multi-population GWA mapping via multi-task regularized regression

paper_content:

MOTIVATION ::: Population heterogeneity through admixing of different founder populations can produce spurious associations in genome-wide association studies that are linked to the population structure rather than the phenotype. Since samples from the same population generally co-evolve, different populations may or may not share the same genetic underpinnings for the seemingly common phenotype. Our goal is to develop a unified framework for detecting causal genetic markers through a joint association analysis of multiple populations. ::: ::: ::: RESULTS ::: Based on a multi-task regression principle, we present a multi-population group lasso algorithm using L(1)/L(2)-regularized regression for joint association analysis of multiple populations that are stratified either via population survey or computational estimation. Our algorithm combines information from genetic markers across populations, to identify causal markers. It also implicitly accounts for correlations between the genetic markers, thus enabling better control over false positive rates. Joint analysis across populations enables the detection of weak associations common to all populations with greater power than in a separate analysis of each population. At the same time, the regression-based framework allows causal alleles that are unique to a subset of the populations to be correctly identified. We demonstrate the effectiveness of our method on HapMap-simulated and lactase persistence datasets, where we significantly outperform state of the art methods, with greater power for detecting weak associations and reduced spurious associations. ::: ::: ::: AVAILABILITY ::: Software will be available at http://www.sailing.cs.cmu.edu/.
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paper_title: A multi-task learning formulation for predicting disease progression

paper_content:

Alzheimer's Disease (AD), the most common type of dementia, is a severe neurodegenerative disorder. Identifying markers that can track the progress of the disease has recently received increasing attentions in AD research. A definitive diagnosis of AD requires autopsy confirmation, thus many clinical/cognitive measures including Mini Mental State Examination (MMSE) and Alzheimer's Disease Assessment Scale cognitive subscale (ADAS-Cog) have been designed to evaluate the cognitive status of the patients and used as important criteria for clinical diagnosis of probable AD. In this paper, we propose a multi-task learning formulation for predicting the disease progression measured by the cognitive scores and selecting markers predictive of the progression. Specifically, we formulate the prediction problem as a multi-task regression problem by considering the prediction at each time point as a task. We capture the intrinsic relatedness among different tasks by a temporal group Lasso regularizer. The regularizer consists of two components including an L2,1-norm penalty on the regression weight vectors, which ensures that a small subset of features will be selected for the regression models at all time points, and a temporal smoothness term which ensures a small deviation between two regression models at successive time points. We have performed extensive evaluations using various types of data at the baseline from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database for predicting the future MMSE and ADAS-Cog scores. Our experimental studies demonstrate the effectiveness of the proposed algorithm for capturing the progression trend and the cross-sectional group differences of AD severity. Results also show that most markers selected by the proposed algorithm are consistent with findings from existing cross-sectional studies.
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paper_title: High-Order Multi-Task Feature Learning to Identify Longitudinal Phenotypic Markers for Alzheimer's Disease Progression Prediction

paper_content:

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by progressive impairment of memory and other cognitive functions. Regression analysis has been studied to relate neuroimaging measures to cognitive status. However, whether these measures have further predictive power to infer a trajectory of cognitive performance over time is still an under-explored but important topic in AD research. We propose a novel high-order multi-task learning model to address this issue. The proposed model explores the temporal correlations existing in imaging and cognitive data by structured sparsity-inducing norms. The sparsity of the model enables the selection of a small number of imaging measures while maintaining high prediction accuracy. The empirical studies, using the longitudinal imaging and cognitive data of the ADNI cohort, have yielded promising results.
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paper_title: A Multi-Task Learning Formulation for Survival Analysis

paper_content:

Predicting the occurrence of a particular event of interest at future time points is the primary goal of survival analysis. The presence of incomplete observations due to time limitations or loss of data traces is known as censoring which brings unique challenges in this domain and differentiates survival analysis from other standard regression methods. The popularly used survival analysis methods such as Cox proportional hazard model and parametric survival regression suffer from some strict assumptions and hypotheses that are not realistic in most of the real-world applications. To overcome the weaknesses of these two types of methods, in this paper, we reformulate the survival analysis problem as a multi-task learning problem and propose a new multi-task learning based formulation to predict the survival time by estimating the survival status at each time interval during the study duration. We propose an indicator matrix to enable the multi-task learning algorithm to handle censored instances and incorporate some of the important characteristics of survival problems such as non-negative non-increasing list structure into our model through max-heap projection. We employ the L2,1-norm penalty which enables the model to learn a shared representation across related tasks and hence select important features and alleviate over-fitting in high-dimensional feature spaces; thus, reducing the prediction error of each task. To efficiently handle the two non-smooth constraints, in this paper, we propose an optimization method which employs Alternating Direction Method of Multipliers (ADMM) algorithm to solve the proposed multi-task learning problem. We demonstrate the performance of the proposed method using real-world microarray gene expression high-dimensional benchmark datasets and show that our method outperforms state-of-the-art methods.
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paper_title: Multi-task learning for cross-platform siRNA efficacy prediction: an in-silico study

paper_content:

BackgroundGene silencing using exogenous small interfering RNAs (siRNAs) is now a widespread molecular tool for gene functional study and new-drug target identification. The key mechanism in this technique is to design efficient siRNAs that incorporated into the RNA-induced silencing complexes (RISC) to bind and interact with the mRNA targets to repress their translations to proteins. Although considerable progress has been made in the computational analysis of siRNA binding efficacy, few joint analysis of different RNAi experiments conducted under different experimental scenarios has been done in research so far, while the joint analysis is an important issue in cross-platform siRNA efficacy prediction. A collective analysis of RNAi mechanisms for different datasets and experimental conditions can often provide new clues on the design of potent siRNAs.ResultsAn elegant multi-task learning paradigm for cross-platform siRNA efficacy prediction is proposed. Experimental studies were performed on a large dataset of siRNA sequences which encompass several RNAi experiments recently conducted by different research groups. By using our multi-task learning method, the synergy among different experiments is exploited and an efficient multi-task predictor for siRNA efficacy prediction is obtained. The 19 most popular biological features for siRNA according to their jointly importance in multi-task learning were ranked. Furthermore, the hypothesis is validated out that the siRNA binding efficacy on different messenger RNAs(mRNAs) have different conditional distribution, thus the multi-task learning can be conducted by viewing tasks at an "mRNA"-level rather than at the "experiment"-level. Such distribution diversity derived from siRNAs bound to different mRNAs help indicate that the properties of target mRNA have important implications on the siRNA binding efficacy.ConclusionsThe knowledge gained from our study provides useful insights on how to analyze various cross-platform RNAi data for uncovering of their complex mechanism.
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paper_title: Novel applications of multitask learning and multiple output regression to multiple genetic trait prediction

paper_content:

Given a set of biallelic molecular markers, such as SNPs, with genotype values encoded numerically on a collection of plant, animal or human samples, the goal of genetic trait prediction is to predict the quantitative trait values by simultaneously modeling all marker effects. Genetic trait prediction is usually represented as linear regression models. In many cases, for the same set of samples and markers, multiple traits are observed. Some of these traits might be correlated with each other. Therefore, modeling all the multiple traits together may improve the prediction accuracy. In this work, we view the multitrait prediction problem from a machine learning angle: as either a multitask learning problem or a multiple output regression problem, depending on whether different traits share the same genotype matrix or not. We then adapted multitask learning algorithms and multiple output regression algorithms to solve the multitrait prediction problem. We proposed a few strategies to improve the least square error of the prediction from these algorithms. Our experiments show that modeling multiple traits together could improve the prediction accuracy for correlated traits. ::: ::: Availability and implementation: The programs we used are either public or directly from the referred authors, such as MALSAR (http://www.public.asu.edu/~jye02/Software/MALSAR/) package. The Avocado data set has not been published yet and is available upon request. ::: ::: Contact: moc.mbi.su@ehd
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paper_title: ProDiGe: Prioritization Of Disease Genes with multitask machine learning from positive and unlabeled examples

paper_content:

Elucidating the genetic basis of human diseases is a central goal of genetics and molecular biology. While traditional linkage analysis and modern high-throughput techniques often provide long lists of tens or hundreds of disease gene candidates, the identification of disease genes among the candidates remains time-consuming and expensive. Efficient computational methods are therefore needed to prioritize genes within the list of candidates, by exploiting the wealth of information available about the genes in various databases. Here we propose ProDiGe, a novel algorithm for Prioritization of Disease Genes. ProDiGe implements a novel machine learning strategy based on learning from positive and unlabeled examples, which allows to integrate various sources of information about the genes, to share information about known disease genes across diseases, and to perform genome-wide searches for new disease genes. Experiments on real data show that ProDiGe outperforms state-of-the-art methods for the prioritization of genes in human diseases.
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paper_title: Leveraging sequence classification by taxonomy-based multitask learning

paper_content:

In this work we consider an inference task that biologists are very good at: deciphering biological processes by bringing together knowledge that has been obtained by experiments using various organisms, while respecting the differences and commonalities of these organisms We look at this problem from an sequence analysis point of view, where we aim at solving the same classification task in different organisms We investigate the challenge of combining information from several organisms, whereas we consider the relation between the organisms to be defined by a tree structure derived from their phylogeny Multitask learning, a machine learning technique that recently received considerable attention, considers the problem of learning across tasks that are related to each other We treat each organism as one task and present three novel multitask learning methods to handle situations in which the relationships among tasks can be described by a hierarchy These algorithms are designed for large-scale applications and are therefore applicable to problems with a large number of training examples, which are frequently encountered in sequence analysis We perform experimental analyses on synthetic data sets in order to illustrate the properties of our algorithms Moreover, we consider a problem from genomic sequence analysis, namely splice site recognition, to illustrate the usefulness of our approach We show that intelligently combining data from 15 eukaryotic organisms can indeed significantly improve the prediction performance compared to traditional learning approaches On a broader perspective, we expect that algorithms like the ones presented in this work have the potential to complement and enrich the strategy of homology-based sequence analysis that are currently the quasi-standard in biological sequence analysis.
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paper_title: Multitask Learning for Brain-Computer Interfaces

paper_content:

Brain-computer interfaces (BCIs) are limited in their applicability in everyday settings by the current necessity to record subjectspecific calibration data prior to actual use of the BCI for communication. In this paper, we utilize the framework of multitask learning to construct a BCI that can be used without any subject-specific calibration process. We discuss how this out-of-the-box BCI can be further improved in a computationally efficient manner as subject-specific data becomes available. The feasibility of the approach is demonstrated on two sets of experimental EEG data recorded during a standard two-class motor imagery paradigm from a total of 19 healthy subjects. Specifically, we show that satisfactory classification results can be achieved with zero training data, and combining prior recordings with subjectspecific calibration data substantially outperforms using subject-specific data only. Our results further show that transfer between recordings under slightly different experimental setups is feasible.
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paper_title: Inferring latent task structure for Multitask Learning by Multiple Kernel Learning

paper_content:

BackgroundThe lack of sufficient training data is the limiting factor for many Machine Learning applications in Computational Biology. If data is available for several different but related problem domains, Multitask Learning algorithms can be used to learn a model based on all available information. In Bioinformatics, many problems can be cast into the Multitask Learning scenario by incorporating data from several organisms. However, combining information from several tasks requires careful consideration of the degree of similarity between tasks. Our proposed method simultaneously learns or refines the similarity between tasks along with the Multitask Learning classifier. This is done by formulating the Multitask Learning problem as Multiple Kernel Learning, using the recently published q-Norm MKL algorithm.ResultsWe demonstrate the performance of our method on two problems from Computational Biology. First, we show that our method is able to improve performance on a splice site dataset with given hierarchical task structure by refining the task relationships. Second, we consider an MHC-I dataset, for which we assume no knowledge about the degree of task relatedness. Here, we are able to learn the task similarities ab initio along with the Multitask classifiers. In both cases, we outperform baseline methods that we compare against.ConclusionsWe present a novel approach to Multitask Learning that is capable of learning task similarity along with the classifiers. The framework is very general as it allows to incorporate prior knowledge about tasks relationships if available, but is also able to identify task similarities in absence of such prior information. Both variants show promising results in applications from Computational Biology.
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paper_title: Deep Model Based Transfer and Multi-Task Learning for Biological Image Analysis

paper_content:

A central theme in learning from image data is to develop appropriate image representations for the specific task at hand. Traditional methods used handcrafted local features combined with high-level image representations to generate image-level representations. Thus, a practical challenge is to determine what features are appropriate for specific tasks. For example, in the study of gene expression patterns in Drosophila melanogaster, texture features based on wavelets were particularly effective for determining the developmental stages from in situ hybridization (ISH) images. Such image representation is however not suitable for controlled vocabulary (CV) term annotation because each CV term is often associated with only a part of an image. Here, we developed problem-independent feature extraction methods to generate hierarchical representations for ISH images. Our approach is based on the deep convolutional neural networks (CNNs) that can act on image pixels directly. To make the extracted features generic, the models were trained using a natural image set with millions of labeled examples. These models were transferred to the ISH image domain and used directly as feature extractors to compute image representations. Furthermore, we employed multi-task learning method to fine-tune the pre-trained models with labeled ISH images, and also extracted features from the fine-tuned models. Experimental results showed that feature representations computed by deep models based on transfer and multi-task learning significantly outperformed other methods for annotating gene expression patterns at different stage ranges. We also demonstrated that the intermediate layers of deep models produced the best gene expression pattern representations.
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paper_title: Sparse multitask regression for identifying common mechanism of response to therapeutic targets

paper_content:

Motivation: Molecular association of phenotypic responses is an important step in hypothesis generation and for initiating design of new experiments. Current practices for associating gene expression data with multidimensional phenotypic data are typically (i) performed one-to-one, i.e. each gene is examined independently with a phenotypic index and (ii) tested with one stress condition at a time, i.e. different perturbations are analyzed separately. As a result, the complex coordination among the genes responsible for a phenotypic profile is potentially lost. More importantly, univariate analysis can potentially hide new insights into common mechanism of response. ::: ::: Results: In this article, we propose a sparse, multitask regression model together with co-clustering analysis to explore the intrinsic grouping in associating the gene expression with phenotypic signatures. The global structure of association is captured by learning an intrinsic template that is shared among experimental conditions, with local perturbations introduced to integrate effects of therapeutic agents. We demonstrate the performance of our approach on both synthetic and experimental data. Synthetic data reveal that the multi-task regression has a superior reduction in the regression error when compared with traditional L1-and L2-regularized regression. On the other hand, experiments with cell cycle inhibitors over a panel of 14 breast cancer cell lines demonstrate the relevance of the computed molecular predictors with the cell cycle machinery, as well as the identification of hidden variables that are not captured by the baseline regression analysis. Accordingly, the system has identified CLCA2 as a hidden transcript and as a common mechanism of response for two therapeutic agents of CI-1040 and Iressa, which are currently in clinical use. ::: ::: Contact: b_parvin@lbl.gov
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paper_title: Multitask Learning for Protein Subcellular Location Prediction

paper_content:

Protein subcellular localization is concerned with predicting the location of a protein within a cell using computational methods. The location information can indicate key functionalities of proteins. Thus, accurate prediction of subcellular localizations of proteins can help the prediction of protein functions and genome annotations, as well as the identification of drug targets. Machine learning methods such as Support Vector Machines (SVMs) have been used in the past for the problem of protein subcellular localization, but have been shown to suffer from a lack of annotated training data in each species under study. To overcome this data sparsity problem, we observe that because some of the organisms may be related to each other, there may be some commonalities across different organisms that can be discovered and used to help boost the data in each localization task. In this paper, we formulate protein subcellular localization problem as one of multitask learning across different organisms. We adapt and compare two specializations of the multitask learning algorithms on 20 different organisms. Our experimental results show that multitask learning performs much better than the traditional single-task methods. Among the different multitask learning methods, we found that the multitask kernels and supertype kernels under multitask learning that share parameters perform slightly better than multitask learning by sharing latent features. The most significant improvement in terms of localization accuracy is about 25 percent. We find that if the organisms are very different or are remotely related from a biological point of view, then jointly training the multiple models cannot lead to significant improvement. However, if they are closely related biologically, the multitask learning can do much better than individual learning.
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paper_title: Joint covariate selection and joint subspace selection for multiple classification problems

paper_content:

We address the problem of recovering a common set of covariates that are relevant simultaneously to several classification problems. By penalizing the sum of ? 2 norms of the blocks of coefficients associated with each covariate across different classification problems, similar sparsity patterns in all models are encouraged. To take computational advantage of the sparsity of solutions at high regularization levels, we propose a blockwise path-following scheme that approximately traces the regularization path. As the regularization coefficient decreases, the algorithm maintains and updates concurrently a growing set of covariates that are simultaneously active for all problems. We also show how to use random projections to extend this approach to the problem of joint subspace selection, where multiple predictors are found in a common low-dimensional subspace. We present theoretical results showing that this random projection approach converges to the solution yielded by trace-norm regularization. Finally, we present a variety of experimental results exploring joint covariate selection and joint subspace selection, comparing the path-following approach to competing algorithms in terms of prediction accuracy and running time.
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paper_title: Sparse Bayesian multi-task learning for predicting cognitive outcomes from neuroimaging measures in Alzheimer's disease

paper_content:

Alzheimer's disease (AD) is the most common form of dementia that causes progressive impairment of memory and other cognitive functions. Multivariate regression models have been studied in AD for revealing relationships between neuroimaging measures and cognitive scores to understand how structural changes in brain can influence cognitive status. Existing regression methods, however, do not explicitly model dependence relation among multiple scores derived from a single cognitive test. It has been found that such dependence can deteriorate the performance of these methods. To overcome this limitation, we propose an efficient sparse Bayesian multi-task learning algorithm, which adaptively learns and exploits the dependence to achieve improved prediction performance. The proposed algorithm is applied to a real world neuroimaging study in AD to predict cognitive performance using MRI scans. The effectiveness of the proposed algorithm is demonstrated by its superior prediction performance over multiple state-of-the-art competing methods and accurate identification of compact sets of cognition-relevant imaging biomarkers that are consistent with prior knowledge.
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paper_title: Multi-task Sequence to Sequence Learning

paper_content:

Sequence to sequence learning has recently emerged as a new paradigm in supervised learning. To date, most of its applications focused on only one task and not much work explored this framework for multiple tasks. This paper examines three multi-task learning (MTL) settings for sequence to sequence models: (a) the oneto-many setting - where the encoder is shared between several tasks such as machine translation and syntactic parsing, (b) the many-to-one setting - useful when only the decoder can be shared, as in the case of translation and image caption generation, and (c) the many-to-many setting - where multiple encoders and decoders are shared, which is the case with unsupervised objectives and translation. Our results show that training on a small amount of parsing and image caption data can improve the translation quality between English and German by up to 1.5 BLEU points over strong single-task baselines on the WMT benchmarks. Furthermore, we have established a new state-of-the-art result in constituent parsing with 93.0 F1. Lastly, we reveal interesting properties of the two unsupervised learning objectives, autoencoder and skip-thought, in the MTL context: autoencoder helps less in terms of perplexities but more on BLEU scores compared to skip-thought.
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paper_title: Collaborative Multi-domain Sentiment Classification

paper_content:

Sentiment classification is a hot research topic in both industrial and academic fields. The mainstream sentiment classification methods are based on machine learning and treat sentiment classification as a text classification problem. However, sentiment classification is widely recognized as a highly domain-dependent task. The sentiment classifier trained in one domain may not perform well in another domain. A simple solution to this problem is training a domain-specific sentiment classifier for each domain. However, it is difficult to label enough data for every domain since they are in a large quantity. In addition, this method omits the sentiment information in other domains. In this paper, we propose to train sentiment classifiers for multiple domains in a collaborative way based on multi-task learning. Specifically, we decompose the sentiment classifier in each domain into two components, a general one and a domain-specific one. The general sentiment classifier can capture the global sentiment information and is trained across various domains to obtain better generalization ability. The domain-specific sentiment classifier is trained using the labeled data in one domain to capture the domain-specific sentiment information. In addition, we explore two kinds of relations between domains, one based on textual content and the other one based on sentiment word distribution. We build a domain similarity graph using domain relations and encode it into our approach as regularization over the domain-specific sentiment classifiers. Besides, we incorporate the sentiment knowledge extracted from sentiment lexicons to help train the general sentiment classifier more accurately. Moreover, we introduce an accelerated optimization algorithm to train the sentiment classifiers efficiently. Experimental results on two benchmark sentiment datasets show that our method can outperform baseline methods significantly and consistently.
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paper_title: A unified architecture for natural language processing: deep neural networks with multitask learning

paper_content:

We describe a single convolutional neural network architecture that, given a sentence, outputs a host of language processing predictions: part-of-speech tags, chunks, named entity tags, semantic roles, semantically similar words and the likelihood that the sentence makes sense (grammatically and semantically) using a language model. The entire network is trained jointly on all these tasks using weight-sharing, an instance of multitask learning. All the tasks use labeled data except the language model which is learnt from unlabeled text and represents a novel form of semi-supervised learning for the shared tasks. We show how both multitask learning and semi-supervised learning improve the generalization of the shared tasks, resulting in state-of-the-art-performance.
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paper_title: Multi-domain Dialog State Tracking using Recurrent Neural Networks

paper_content:

Dialog state tracking is a key component of many modern dialog systems, most of which are designed with a single, well-defined domain in mind. This paper shows that dialog data drawn from different dialog domains can be used to train a general belief tracking model which can operate across all of these domains, exhibiting superior performance to each of the domain-specific models. We propose a training procedure which uses out-of-domain data to initialise belief tracking models for entirely new domains. This procedure leads to improvements in belief tracking performance regardless of the amount of in-domain data available for training the model.
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paper_title: Deep neural networks employing Multi-Task Learning and stacked bottleneck features for speech synthesis

paper_content:

Deep neural networks (DNNs) use a cascade of hidden representations to enable the learning of complex mappings from input to output features. They are able to learn the complex mapping from text-based linguistic features to speech acoustic features, and so perform text-to-speech synthesis. Recent results suggest that DNNs can produce more natural synthetic speech than conventional HMM-based statistical parametric systems. In this paper, we show that the hidden representation used within a DNN can be improved through the use of Multi-Task Learning, and that stacking multiple frames of hidden layer activations (stacked bottleneck features) also leads to improvements. Experimental results confirmed the effectiveness of the proposed methods, and in listening tests we find that stacked bottleneck features in particular offer a significant improvement over both a baseline DNN and a benchmark HMM system.
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paper_title: Feature Constrained Multi-Task Learning Models for Spatiotemporal Event Forecasting

paper_content:

Spatial event forecasting from social media is potentially extremely useful but suffers from critical challenges, such as the dynamic patterns of features (keywords) and geographic heterogeneity (e.g., spatial correlations, imbalanced samples, and different populations in different locations). Most existing approaches (e.g., LASSO regression, dynamic query expansion, and burst detection) address some, but not all, of these challenges. Here, we propose a novel multi-task learning framework that aims to concurrently address all the challenges involved. Specifically, given a collection of locations (e.g., cities), forecasting models are built for all the locations simultaneously by extracting and utilizing appropriate shared information that effectively increases the sample size for each location, thus improving the forecasting performance. The new model combines both static features derived from a predefined vocabulary by domain experts and dynamic features generated from dynamic query expansion in a multi-task feature learning framework. Different strategies to balance homogeneity and diversity between static and dynamic terms are also investigated. And, efficient algorithms based on Iterative Group Hard Thresholding are developed to achieve efficient and effective model training and prediction. Extensive experimental evaluations on Twitter data from civil unrest and influenza outbreak datasets demonstrate the effectiveness and efficiency of our proposed approach.
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paper_title: Fusion of multiple parameterisations for DNN-based sinusoidal speech synthesis with multi-task learning.

paper_content:

It has recently been shown that deep neural networks (DNN) can improve the quality of statistical parametric speech synthesis (SPSS) when using a source-filter vocoder. Our own previous work has furthermore shown that a dynamic sinusoidal model (DSM) is also highly suited to DNN-based SPSS, whereby sinusoids may either be used themselves as a “direct parameterisation” (DIR), or they may be encoded using an “intermediate spectral parameterisation” (INT). The approach in that work was effectively to replace a decision tree with a neural network. However, waveform parameterisation and synthesis steps that have been developed to suit HMMs may not fully exploit DNN capabilities. Here, in contrast, we investigate ways to combine INT and DIR at the levels of both DNN modelling and waveform generation. For DNN training, we propose to use multi-task learning to model cepstra (from INT) and log amplitudes (from DIR) as primary and secondary tasks. Our results show combining these improves modelling accuracy for both tasks. Next, during synthesis, instead of discarding parameters from the second task, a fusion method using harmonic amplitudes derived from both tasks is applied. Preference tests show the proposed method gives improved performance, and that this applies to synthesising both with and without global variance parameters.
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paper_title: Regularized multi--task learning

paper_content:

Past empirical work has shown that learning multiple related tasks from data simultaneously can be advantageous in terms of predictive performance relative to learning these tasks independently. In this paper we present an approach to multi--task learning based on the minimization of regularization functionals similar to existing ones, such as the one for Support Vector Machines (SVMs), that have been successfully used in the past for single--task learning. Our approach allows to model the relation between tasks in terms of a novel kernel function that uses a task--coupling parameter. We implement an instance of the proposed approach similar to SVMs and test it empirically using simulated as well as real data. The experimental results show that the proposed method performs better than existing multi--task learning methods and largely outperforms single--task learning using SVMs.
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paper_title: Multi-task learning for learning to rank in web search

paper_content:

Both the quality and quantity of training data have significant impact on the performance of ranking functions in the context of learning to rank for web search. Due to resource constraints, training data for smaller search engine markets are scarce and we need to leverage existing training data from large markets to enhance the learning of ranking function for smaller markets. In this paper, we present a boosting framework for learning to rank in the multi-task learning context for this purpose. In particular, we propose to learn non-parametric common structures adaptively from multiple tasks in a stage-wise way. An algorithm is developed to iteratively discover super-features that are effective for all the tasks. The estimation of the functions for each task is then learned as a linear combination of those super-features. We evaluate the performance of this multi-task learning method for web search ranking using data from a search engine. Our results demonstrate that multi-task learning methods bring significant relevance improvements over existing baseline methods.
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paper_title: Scalable hierarchical multitask learning algorithms for conversion optimization in display advertising

paper_content:

Many estimation tasks come in groups and hierarchies of related problems. In this paper we propose a hierarchical model and a scalable algorithm to perform inference for multitask learning. It infers task correlation and subtask structure in a joint sparse setting. Implementation is achieved by a distributed subgradient oracle and the successive application of prox-operators pertaining to groups and subgroups of variables. We apply this algorithm to conversion optimization in display advertising. Experimental results on over 1TB data for up to 1 billion observations and 1 million attributes show that the algorithm provides significantly better prediction accuracy while simultaneously beingefficiently scalable by distributed parameter synchronization.
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paper_title: Multi-task learning for boosting with application to web search ranking

paper_content:

In this paper we propose a novel algorithm for multi-task learning with boosted decision trees. We learn several different learning tasks with a joint model, explicitly addressing the specifics of each learning task with task-specific parameters and the commonalities between them through shared parameters. This enables implicit data sharing and regularization. We evaluate our learning method on web-search ranking data sets from several countries. Here, multitask learning is particularly helpful as data sets from different countries vary largely in size because of the cost of editorial judgments. Our experiments validate that learning various tasks jointly can lead to significant improvements in performance with surprising reliability.
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paper_title: A Convex Formulation for Learning Task Relationships in Multi-Task Learning

paper_content:

Multi-task learning is a learning paradigm which seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this paper, we propose a regularization formulation for learning the relationships between tasks in multi-task learning. This formulation can be viewed as a novel generalization of the regularization framework for single-task learning. Besides modeling positive task correlation, our method, called multi-task relationship learning (MTRL), can also describe negative task correlation and identify outlier tasks based on the same underlying principle. Under this regularization framework, the objective function of MTRL is convex. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multi-task learning setting and then generalize it to the asymmetric setting as well. We also study the relationships between MTRL and some existing multi-task learning methods. Experiments conducted on a toy problem as well as several benchmark data sets demonstrate the effectiveness of MTRL.
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paper_title: Multi-Domain Collaborative Filtering

paper_content:

Collaborative filtering is an effective recommendation approach in which the preference of a user on an item is predicted based on the preferences of other users with similar interests. A big challenge in using collaborative filtering methods is the data sparsity problem which often arises because each user typically only rates very few items and hence the rating matrix is extremely sparse. In this paper, we address this problem by considering multiple collaborative filtering tasks in different domains simultaneously and exploiting the relationships between domains. We refer to it as a multi-domain collaborative filtering (MCF) problem. To solve the MCF problem, we propose a probabilistic framework which uses probabilistic matrix factorization to model the rating problem in each domain and allows the knowledge to be adaptively transferred across different domains by automatically learning the correlation between domains. We also introduce the link function for different domains to correct their biases. Experiments conducted on several real-world applications demonstrate the effectiveness of our methods when compared with some representative methods.
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paper_title: Web-scale multi-task feature selection for behavioral targeting

paper_content:

A typical behavioral targeting system optimizing purchase activities, called conversions, faces two main challenges: the web-scale amounts of user histories to process on a daily basis, and the relative sparsity of conversions. In this paper, we try to address these challenges through feature selection. We formulate a multi-task (or group) feature-selection problem among a set of related tasks (sharing a common set of features), namely advertising campaigns. We apply a group-sparse penalty consisting of a combination of an l1 and l2 penalty and an associated fast optimization algorithm for distributed parameter estimation. Our algorithm relies on a variant of the well known Fast Iterative Thresholding Algorithm (FISTA), a closed-form solution for mixed norm programming and a distributed subgradient oracle. To efficiently handle web-scale user histories, we present a distributed inference algorithm for the problem that scales to billions of instances and millions of attributes. We show the superiority of our algorithm in terms of both sparsity and ROC performance over baseline feature selection methods (both single-task -regularization and multi-task mutual-information gain).
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paper_title: Efficient multi-task feature learning with calibration

paper_content:

Multi-task feature learning has been proposed to improve the generalization performance by learning the shared features among multiple related tasks and it has been successfully applied to many real-world problems in machine learning, data mining, computer vision and bioinformatics. Most existing multi-task feature learning models simply assume a common noise level for all tasks, which may not be the case in real applications. Recently, a Calibrated Multivariate Regression (CMR) model has been proposed, which calibrates different tasks with respect to their noise levels and achieves superior prediction performance over the non-calibrated one. A major challenge is how to solve the CMR model efficiently as it is formulated as a composite optimization problem consisting of two non-smooth terms. In this paper, we propose a variant of the calibrated multi-task feature learning formulation by including a squared norm regularizer. We show that the dual problem of the proposed formulation is a smooth optimization problem with a piecewise sphere constraint. The simplicity of the dual problem enables us to develop fast dual optimization algorithms with low per-iteration cost. We also provide a detailed convergence analysis for the proposed dual optimization algorithm. Empirical studies demonstrate that, the dual optimization algorithm quickly converges and it is much more efficient than the primal optimization algorithm. Moreover, the calibrated multi-task feature learning algorithms with and without the squared norm regularizer achieve similar prediction performance and both outperform the non-calibrated ones. Thus, the proposed variant not only enables us to develop fast optimization algorithms, but also keeps the superior prediction performance of the calibrated multi-task feature learning over the non-calibrated one.
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paper_title: A Regularization Approach to Learning Task Relationships in Multitask Learning

paper_content:

Multitask learning is a learning paradigm that seeks to improve the generalization performance of a learning task with the help of some other related tasks. In this article, we propose a regularization approach to learning the relationships between tasks in multitask learning. This approach can be viewed as a novel generalization of the regularized formulation for single-task learning. Besides modeling positive task correlation, our approach—multitask relationship learning (MTRL)—can also describe negative task correlation and identify outlier tasks based on the same underlying principle. By utilizing a matrix-variate normal distribution as a prior on the model parameters of all tasks, our MTRL method has a jointly convex objective function. For efficiency, we use an alternating method to learn the optimal model parameters for each task as well as the relationships between tasks. We study MTRL in the symmetric multitask learning setting and then generalize it to the asymmetric setting as well. We also discuss some variants of the regularization approach to demonstrate the use of other matrix-variate priors for learning task relationships. Moreover, to gain more insight into our model, we also study the relationships between MTRL and some existing multitask learning methods. Experiments conducted on a toy problem as well as several benchmark datasets demonstrate the effectiveness of MTRL as well as its high interpretability revealed by the task covariance matrix.
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paper_title: Multi � Task Learning for Stock Selection

paper_content:

Artificial Neural Networks can be used to predict future returns of stocks in order to take financial decisions. Should one build a separate network for each stock or share the same network for all the stocks? In this paper we also explore other alternatives, in which some layers are shared and others are not shared. When the prediction of future returns for different stocks are viewed as different tasks, sharing some parameters across stocks is a form of multi-task learning. In a series of experiments with Canadian stocks, we obtain yearly returns that are more than 14% above various benchmarks.
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paper_title: Multi-task Gaussian process learning of robot inverse dynamics

paper_content:

The inverse dynamics problem for a robotic manipulator is to compute the torques needed at the joints to drive it along a given trajectory; it is beneficial to be able to learn this function for adaptive control. A robotic manipulator will often need to be controlled while holding different loads in its end effector, giving rise to a multi-task learning problem. By placing independent Gaussian process priors over the latent functions of the inverse dynamics, we obtain a multi-task Gaussian process prior for handling multiple loads, where the inter-task similarity depends on the underlying inertial parameters. Experiments demonstrate that this multi-task formulation is effective in sharing information among the various loads, and generally improves performance over either learning only on single tasks or pooling the data over all tasks.
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paper_title: Robust Dynamic Trajectory Regression on Road Networks: A Multi-task Learning Framework

paper_content:

Trajectory regression, which aims to predict the travel time of arbitrary trajectories on road networks, attracts significant attention in various applications of traffic systems these years. In this paper, we tackle this problem with a multitask learning (MTL) framework. To take the temporal nature of the problem into consideration, we divide the regression problem into a set of sub-tasks of distinct time periods, then the problem can be treated in a multi-task learning framework. Further, we propose a novel regularization term in which we exploit the block sparse structure to augment the robustness of the model. In addition, we incorporate the spatial smoothness over road links and thus achieve a spatial-temporal framework. An accelerated proximal algorithm is adopted to solve the convex but non-smooth problem, which will converge to the global optimum. Experiments on both synthetic and real data sets demonstrate the effectiveness of the proposed method.
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paper_title: Transferring MultiDevice Localization Models Using Latent Multi-Task Learning

paper_content:

In this paper, we propose a latent multi-task learning algorithm to solve the multi-device indoor localization problem. Traditional indoor localization systems often assume that the collected signal data distributions are fixed, and thus the localization model learned on one device can be used on other devices without adaptation. However, by empirically studying the signal variation over different devices, we found this assumption to be invalid in practice. To solve this problem, we treat multiple devices as multiple learning tasks, and propose a multi-task learning algorithm. Different from algorithms assuming that the hypotheses learned from the original data space for related tasks can be similar, we only require the hypotheses learned in a latent feature space are similar. To establish our algorithm, we employ an alternating optimization approach to iteratively learn feature mappings and multi-task regression models for the devices. We apply our latent multi-task learning algorithm to real-world indoor localization data and demonstrate its effectiveness.
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paper_title: Time-dependent trajectory regression on road networks via multi-task learning

paper_content:

Road travel costs are important knowledge hidden in large-scale GPS trajectory data sets, the discovery of which can benefit many applications such as intelligent route planning and automatic driving navigation. While there are previous studies which tackled this task by modeling it as a regression problem with spatial smoothness taken into account, they unreasonably assumed that the latent cost of each road remains unchanged over time. Other works on route planning and recommendation that have considered temporal factors simply assumed that the temporal dynamics be known in advance as a parametric function over time, which is not faithful to reality. To overcome these limitations, in this paper, we propose an extension to a previous static trajectory regression framework by learning the temporal dynamics of road travel costs in an innovative non-parametric manner which can effectively overcome the temporal sparsity problem. In particular, we unify multiple different trajectory regression problems in a multi-task framework by introducing a novel crosstask regularization which encourages temporal smoothness on the change of road travel costs. We then propose an efficient block coordinate descent method to solve the resulting problem by exploiting its separable structures and prove its convergence to global optimum. Experiments conducted on both synthetic and real data sets demonstrate the effectiveness of our method and its improved accuracy on travel time prediction.
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paper_title: Traffic Sign Recognition via Multi-Modal Tree-Structure Embedded Multi-Task Learning

paper_content:

Traffic sign recognition is a rather challenging task for intelligent transportation systems since signs in different subsets, e.g., speed limit signs, prohibition signs, and mandatory signs, are very different from each other in color or shape, whereas they share some similarities to the ones in the same subset. Therefore, it is important to integrate different modalities of visual features, such as color and shape, and select discriminative features for better sign description; in addition, it benefits to explore the correlations between the classes of traffic signs to learn the classifiers jointly to improve the generalization performance. In this paper, we propose M ulti- M odal t ree-structure embedded M ulti- T ask L earning called $\text{M}^{2}$ - tMTL to select discriminative visual features both between and within modalities, as well as the correlated features shared by similar classification tasks. Our method simultaneously introduces two structured sparsity-induced norms into a least squares regression. One of the norms can be used not only to select modality of features but also to conduct within-modality feature selection. Moreover, the hierarchical correlations among the classification tasks are well represented by a tree structure, and therefore, the tree-structure sparsity-induced norm is used for learning the regression coefficients jointly to boost the performance of multi-class traffic sign recognition. Alternating direction method of multipliers (ADMM) is used to efficiently solve the proposed model with guaranteed convergence. Extensive experiments on public benchmark data sets demonstrate that the proposed algorithm leads to a quite interpretable model, and it has better or competitive performance with several state-of-the-art methods but with less computational and memory cost.
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paper_title: Trace Norm Regularization: Reformulations, Algorithms, and Multi-task Learning

paper_content:

We consider a recently proposed optimization formulation of multi-task learning based on trace norm regularized least squares. While this problem may be formulated as a semidefinite program (SDP), its size is beyond general SDP solvers. Previous solution approaches apply proximal gradient methods to solve the primal problem. We derive new primal and dual reformulations of this problem, including a reduced dual formulation that involves minimizing a convex quadratic function over an operator-norm ball in matrix space. This reduced dual problem may be solved by gradient-projection methods, with each projection involving a singular value decomposition. The dual approach is compared with existing approaches and its practical effectiveness is illustrated on simulations and an application to gene expression pattern analysis.
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paper_title: Regularized multi--task learning

paper_content:

Past empirical work has shown that learning multiple related tasks from data simultaneously can be advantageous in terms of predictive performance relative to learning these tasks independently. In this paper we present an approach to multi--task learning based on the minimization of regularization functionals similar to existing ones, such as the one for Support Vector Machines (SVMs), that have been successfully used in the past for single--task learning. Our approach allows to model the relation between tasks in terms of a novel kernel function that uses a task--coupling parameter. We implement an instance of the proposed approach similar to SVMs and test it empirically using simulated as well as real data. The experimental results show that the proposed method performs better than existing multi--task learning methods and largely outperforms single--task learning using SVMs.
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paper_title: Multi-task and Lifelong Learning of Kernels

paper_content:

We consider a problem of learning kernels for use in SVM classification in the multi-task and lifelong scenarios and provide generalization bounds on the error of a large margin classifier. Our results show that, under mild conditions on the family of kernels used for learning, solving several related tasks simultaneously is beneficial over single task learning. In particular, as the number of observed tasks grows, assuming that in the considered family of kernels there exists one that yields low approximation error on all tasks, the overhead associated with learning such a kernel vanishes and the complexity converges to that of learning when this good kernel is given to the learner.
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paper_title: Exploiting Task Relatedness for Multiple Task Learning

paper_content:

The approach of learning of multiple “related” tasks simultaneously has proven quite successful in practice; however, theoretical justification for this success has remained elusive. The starting point for previous work on multiple task learning has been that the tasks to be learned jointly are somehow “algorithmically related”, in the sense that the results of applying a specific learning algorithm to these tasks are assumed to be similar. We offer an alternative approach, defining relatedness of tasks on the basis of similarity between the example generating distributions that underline these task.
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paper_title: Estimating relatedness via data compression

paper_content:

We show that it is possible to use data compression on independently obtained hypotheses from various tasks to algorithmically provide guarantees that the tasks are sufficiently related to benefit from multitask learning. We give uniform bounds in terms of the empirical average error for the true average error of the n hypotheses provided by deterministic learning algorithms drawing independent samples from a set of n unknown computable task distributions over finite sets.
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paper_title: Multi-task learning and algorithmic stability

paper_content:

In this paper, we study multi-task algorithms from the perspective of the algorithmic stability. We give a definition of the multi-task uniform stability, a generalization of the conventional uniform stability, which measures the maximum difference between the loss of a multi-task algorithm trained on a data set and that of the multitask algorithm trained on the same data set but with a data point removed in each task. In order to analyze multi-task algorithms based on multi-task uniform stability, we prove a generalized McDiarmid's inequality which assumes the difference bound condition holds by changing multiple input arguments instead of only one in the conventional McDiarmid's inequality. By using the generalized McDiarmid's inequality as a tool, we can analyze the generalization performance of general multitask algorithms in terms of the multi-task uniform stability. Moreover, as applications, we prove generalization bounds of several representative regularized multi-task algorithms.
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paper_title: Support union recovery in high-dimensional multivariate regression

paper_content:

multivariate group Lasso, in which block regularization based on the ‘1/‘2 norm is used for support union recovery, or recovery of the set of s rows for which B is non-zero. Under high-dimensional scaling, we show that the multivariate group Lasso exhibits a threshold for the recovery of the exact row pattern with high probability over the random design and noise that is specified by the sample complexity parameter (n,p,s) := n/[2 (B )log(p s)]. Here n is the sample size, and (B ) is a sparsity-overlap function measuring a combination of the sparsities and overlaps of the K-regression coecient vectors that constitute the model. We prove that the multivariate group Lasso succeeds for problem sequences (n,p,s) such that (n,p,s) exceeds a critical level u, and fails for sequences such that (n,p,s) lies below a critical level ‘. For the special case of the standard Gaussian ensemble, we show that ‘ = u so that the characterization is sharp. The sparsity-overlap function (B ) reveals that, if the design is uncorrelated on the active rows, ‘1/‘2 regularization for multivariate regression never harms performance relative to an ordinary Lasso approach, and can yield substantial improvements in sample complexity (up to a factor of K) when the regression vectors are suitably orthogonal. For more general designs, it is possible for the ordinary Lasso to outperform the multivariate group Lasso. We complement our analysis with simulations that demonstrate the sharpness of our theoretical results, even for relatively small problems.
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paper_title: A notion of task relatedness yielding provable multiple-task learning guarantees

paper_content:

The approach of learning multiple "related" tasks simultaneously has proven quite successful in practice; however, theoretical justification for this success has remained elusive. The starting point for previous work on multiple task learning has been that the tasks to be learned jointly are somehow "algorithmically related", in the sense that the results of applying a specific learning algorithm to these tasks are assumed to be similar. We offer an alternative approach, defining relatedness of tasks on the basis of similarity between the example generating distributions that underlie these tasks. ::: ::: We provide a formal framework for this notion of task relatedness, which captures a sub-domain of the wide scope of issues in which one may apply a multiple task learning approach. Our notion of task similarity is relevant to a variety of real life multitask learning scenarios and allows the formal derivation of generalization bounds that are strictly stronger than the previously known bounds for both the learning-to-learn and the multitask learning scenarios. We give precise conditions under which our bounds guarantee generalization on the basis of smaller sample sizes than the standard single-task approach.
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paper_title: Learning Incoherent Sparse and Low-Rank Patterns from Multiple Tasks

paper_content:

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multitask learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is nonconvex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose employing the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is nondifferentiable and the feasible domain is nontrivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of the projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and a Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in detail. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multitask learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multitask learning formulation and the efficiency of the proposed projected gradient algorithms.
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paper_title: Taking Advantage of Sparsity in Multi-Task Learning

paper_content:

We study the problem of estimating multiple linear regression equations for the purpose of both prediction and variable selection. Following recent work on multi-task learning Argyriou et al. [2008], we assume that the regression vectors share the same sparsity pattern. This means that the set of relevant predictor variables is the same across the different equations. This assumption leads us to consider the Group Lasso as a candidate estimation method. We show that this estimator enjoys nice sparsity oracle inequalities and variable selection properties. The results hold under a certain restricted eigenvalue condition and a coherence condition on the design matrix, which naturally extend recent work in Bickel et al. [2007], Lounici [2008]. In particular, in the multi-task learning scenario, in which the number of tasks can grow, we are able to remove completely the effect of the number of predictor variables in the bounds. Finally, we show how our results can be extended to more general noise distributions, of which we only require the variance to be finite.
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paper_title: Learning Multiple Tasks with Kernel Methods

paper_content:

We study the problem of learning many related tasks simultaneously using kernel methods and regularization. The standard single-task kernel methods, such as support vector machines and regularization networks, are extended to the case of multi-task learning. Our analysis shows that the problem of estimating many task functions with regularization can be cast as a single task learning problem if a family of multi-task kernel functions we define is used. These kernels model relations among the tasks and are derived from a novel form of regularizers. Specific kernels that can be used for multi-task learning are provided and experimentally tested on two real data sets. In agreement with past empirical work on multi-task learning, the experiments show that learning multiple related tasks simultaneously using the proposed approach can significantly outperform standard single-task learning particularly when there are many related tasks but few data per task.
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paper_title: Excess risk bounds for multitask learning with trace norm regularization

paper_content:

Trace norm regularization is a popular method of multitask learning. We give excess risk bounds with explicit dependence on the number of tasks, the number of examples per task and properties of the data distribution. The bounds are independent of the dimension of the input space, which may be infinite as in the case of reproducing kernel Hilbert spaces. A byproduct of the proof are bounds on the expected norm of sums of random positive semidefinite matrices with subexponential moments.
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paper_title: Bounds for linear multi-task learning

paper_content:

We give dimension-free and data-dependent bounds for linear multi-task learning where a common linear operator is chosen to preprocess data for a vector of task specific linear-thresholding classifiers. The complexity penalty of multi-task learning is bounded by a simple expression involving the margins of the task-specific classifiers, the Hilbert-Schmidt norm of the selected preprocessor and the Hilbert-Schmidt norm of the covariance operator for the total mixture of all task distributions, or, alternatively, the Frobenius norm of the total Gramian matrix for the data-dependent version. The results can be compared to state-of-the-art results on linear single-task learning.
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paper_title: Multi-task Regression using Minimal Penalties

paper_content:

In this paper we study the kernel multiple ridge regression framework, which we refer to as multitask regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal calibration is the covariance matrix of the noise between the different tasks. We present a new algorithm to estimate this covariance matrix, based on the concept of minimal penalty, which was previously used in the single-task regression framework to estimate the variance of the noise. We show, in a non-asymptotic setting and under mild assumptions on the target function, that this estimator converges towards the covariance matrix. Then plugging this estimator into the corresponding ideal penalty leads to an oracle inequality. We illustrate the behavior of our algorithm on synthetic examples.
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paper_title: Learning Multiple Tasks using Shared Hypotheses

paper_content:

In this work we consider a setting where we have a very large number of related tasks with few examples from each individual task. Rather than either learning each task individually (and having a large generalization error) or learning all the tasks together using a single hypothesis (and suffering a potentially large inherent error), we consider learning a small pool of shared hypotheses. Each task is then mapped to a single hypothesis in the pool (hard association). We derive VC dimension generalization bounds for our model, based on the number of tasks, shared hypothesis and the VC dimension of the hypotheses class. We conducted experiments with both synthetic problems and sentiment of reviews, which strongly support our approach.
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paper_title: On spectral learning

paper_content:

In this paper, we study the problem of learning a matrix W from a set of linear measurements. Our formulation consists in solving an optimization problem which involves regularization with a spectral penalty term. That is, the penalty term is a function of the spectrum of the covariance of W. Instances of this problem in machine learning include multi-task learning, collaborative filtering and multi-view learning, among others. Our goal is to elucidate the form of the optimal solution of spectral learning. The theory of spectral learning relies on the von Neumann characterization of orthogonally invariant norms and their association with symmetric gauge functions. Using this tool we formulate a representer theorem for spectral regularization and specify it to several useful example, such as Schatten p-norms, trace norm and spectral norm, which should proved useful in applications.
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paper_title: Union Support Recovery in Multi-task Learning

paper_content:

We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix complicate the analysis. A clearer and simpler picture emerges by studying the Normal means model. This model, often used in the field of statistics, is a simplified model that provides a laboratory for studying complex procedures.
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paper_title: The Benefit of Multitask Representation Learning

paper_content:

We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case of linear feature learning. Conditions on the theoretical advantage offered by multitask representation learning over independent task learning are established. In particular, focusing on the important example of half-space learning, we derive the regime in which multitask representation learning is beneficial over independent task learning, as a function of the sample size, the number of tasks and the intrinsic data dimensionality. Other potential applications of our results include multitask feature learning in reproducing kernel Hilbert spaces and multilayer, deep networks.
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paper_title: A theoretical framework for learning from a pool of disparate data sources

paper_content:

Many enterprises incorporate information gathered from a variety of data sources into an integrated input for some learning task. For example, aiming towards the design of an automated diagnostic tool for some disease, one may wish to integrate data gathered in many different hospitals. A major obstacle to such endeavors is that different data sources may vary considerably in the way they choose to represent related data. In practice, the problem is usually solved by a manual construction of semantic mappings and translations between the different sources. Recently there have been attempts to introduce automated algorithms based on machine learning tools for the construction of such translations.In this work we propose a theoretical framework for making classification predictions from a collection of different data sources, without creating explicit translations between them. Our framework allows a precise mathematical analysis of the complexity of such tasks, and it provides a tool for the development and comparison of different learning algorithms. Our main objective, at this stage, is to demonstrate the usefulness of computational learning theory to this practically important area and to stimulate further theoretical and experimental research of questions related to this framework.
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paper_title: When is there a representer theorem? Vector versus matrix regularizers

paper_content:

We consider a general class of regularization methods which learn a vector of parameters on the basis of linear measurements. It is well known that if the regularizer is a nondecreasing function of the inner product then the learned vector is a linear combination of the input data. This result, known as the {\em representer theorem}, is at the basis of kernel-based methods in machine learning. In this paper, we prove the necessity of the above condition, thereby completing the characterization of kernel methods based on regularization. We further extend our analysis to regularization methods which learn a matrix, a problem which is motivated by the application to multi-task learning. In this context, we study a more general representer theorem, which holds for a larger class of regularizers. We provide a necessary and sufficient condition for these class of matrix regularizers and highlight them with some concrete examples of practical importance. Our analysis uses basic principles from matrix theory, especially the useful notion of matrix nondecreasing function.
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paper_title: Multi-level Lasso for Sparse Multi-task Regression

paper_content:

We present a flexible formulation for variable selection in multi-task regression to allow for discrepancies in the estimated sparsity patterns accross the multiple tasks, while leveraging the common structure among them. Our approach is based on an intuitive decomposition of the regression coe_cients into a product between a component that is common to all tasks and another component that captures task-specificity. This decomposition yields the Multi-level Lasso objective that can be solved efficiently via alternating optimization. The analysis of the "orthonormal design" case reveals some interesting insights on the nature of the shrinkage performed by our method, compared to that of related work. Theoretical guarantees are provided on the consistency of Multi-level Lasso. Simulations and empirical study of micro-array data further demonstrate the value of our framework.
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paper_title: The rademacher complexity of linear transformation classes

paper_content:

Bounds are given for the empirical and expected Rademacher complexity of classes of linear transformations from a Hilbert space H to a finite dimensional space. The results imply generalization guarantees for graph regularization and multi-task subspace learning.
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paper_title: Spike and slab variational inference for multi-task and multiple kernel learning

paper_content:

We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi-task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multi-output Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.
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paper_title: A framework for learning predictive structures from multiple tasks and unlabeled data

paper_content:

One of the most important issues in machine learning is whether one can improve the performance of a supervised learning algorithm by including unlabeled data. Methods that use both labeled and unlabeled data are generally referred to as semi-supervised learning. Although a number of such methods are proposed, at the current stage, we still don't have a complete understanding of their effectiveness. This paper investigates a closely related problem, which leads to a novel approach to semi-supervised learning. Specifically we consider learning predictive structures on hypothesis spaces (that is, what kind of classifiers have good predictive power) from multiple learning tasks. We present a general framework in which the structural learning problem can be formulated and analyzed theoretically, and relate it to learning with unlabeled data. Under this framework, algorithms for structural learning will be proposed, and computational issues will be investigated. Experiments will be given to demonstrate the effectiveness of the proposed algorithms in the semi-supervised learning setting.
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paper_title: Sparse coding for multitask and transfer learning

paper_content:

We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear combinations of the atoms of a dictionary on a high or infinite dimensional space. This assumption, together with the large quantity of available data in the multitask and transfer learning settings, allows a principled choice of the dictionary. We provide bounds on the generalization error of this approach, for both settings. Numerical experiments on one synthetic and two real datasets show the advantage of our method over single task learning, a previous method based on orthogonal and dense representation of the tasks and a related method learning task grouping.
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Title: A Survey on Multi-Task Learning

Section 1: INTRODUCTION
Description 1: Introduce the importance and challenges of Multi-Task Learning (MTL), its definition, and a comparison with transfer learning.

Section 2: MTL ALGORITHMS
Description 2: Define MTL and categorize different MTL algorithms into feature learning approach, low-rank approach, task clustering approach, task relation learning approach, dirty approach, multi-level approach, and deep learning approach.

Section 3: Feature Learning Approach
Description 3: Explain the two subcategories of the feature learning approach: feature transformation and feature selection methods.

Section 4: Low-Rank Approach
Description 4: Discuss the low-rank approach in MTL, its assumptions, and its methodology.

Section 5: Task Clustering Approach
Description 5: Describe the task clustering approach which groups similar tasks into clusters and its benefits.

Section 6: Task Relation Learning Approach
Description 6: Explore how task relations are learned automatically from data, and quantify relatedness by task similarity, task correlation, and task covariance.

Section 7: Dirty Approach
Description 7: Explain the dirty approach which decomposes the parameter matrix into two component matrices and its different regularizations.

Section 8: Multi-Level Approach
Description 8: Introduce the multi-level approach which extends the dirty approach and provides more expressive power for modeling complex task structures.

Section 9: Deep Learning Approach
Description 9: Discuss how deep learning models are used in MTL, focusing on shared hidden layers and learning task relations with deep networks.

Section 10: Comparison among Different Approaches
Description 10: Compare different MTL approaches based on their characteristics, robustness, interpretability, and performance.

Section 11: Another Taxonomy for Regularized MTL Methods
Description 11: Present another taxonomy categorizing regularized MTL methods into learning with feature covariance and learning with task relations.

Section 12: Novel Settings in MTL
Description 12: Address novel settings in MTL where conventional assumptions like identical feature representations and binary classification do not hold.

Section 13: MTL WITH OTHER LEARNING PARADIGMS
Description 13: Review the combinations of MTL with unsupervised learning, semi-supervised learning, active learning, reinforcement learning, multi-view learning, and graphical models.

Section 14: HANDLING BIG DATA
Description 14: Discuss how to handle big data in MTL through online, parallel, distributed MTL methods, feature selection, dimensionality reduction, and feature hashing.

Section 15: APPLICATIONS
Description 15: Highlight applications of MTL across various domains such as computer vision, bioinformatics, health informatics, speech and natural language processing, web applications, and ubiquitous computing.

Section 16: THEORETICAL ANALYSES
Description 16: Review the theoretical aspects of MTL, such as generalization bounds, stability, and conditions for recovering true features.

Section 17: CONCLUSIONS
Description 17: Summarize the overall insights of MTL, outlining future directions and addressing the challenges and potential improvements in the field.