Heterogeneous Multi-Task Gaussian Cox Processes
Feng Zhou Quyu Kong Zhijie Deng Fengxiang He Peng Cui Jun Zhu
This paper presents a novel extension of multi-task Gaussian Cox processes
for modeling multiple heterogeneous correlated tasks jointly, e.g.,
classification and regression, via multi-output Gaussian processes (MOGP). A
MOGP prior over the parameters of the dedicated likelihoods for classification,
regression and point process tasks can facilitate sharing of information
between heterogeneous tasks, while allowing for nonparametric parameter
estimation. To circumvent the non-conjugate Bayesian inference in the MOGP
modulated heterogeneous multi-task framework, we employ the data augmentation
technique and derive a mean-field approximation to realize closed-form
iterative updates for estimating model parameters. We demonstrate the
performance and inference on both 1D synthetic data as well as 2D urban data of
Vancouver.