Non-Parametric Representation Learning with Kernels
Pascal Esser Maximilian Fleissner Debarghya Ghoshdastidar
Unsupervised and self-supervised representation learning has become popular
in recent years for learning useful features from unlabelled data.
Representation learning has been mostly developed in the neural network
literature, and other models for representation learning are surprisingly
unexplored. In this work, we introduce and analyze several kernel-based
representation learning approaches: Firstly, we define two kernel
Self-Supervised Learning (SSL) models using contrastive loss functions and
secondly, a Kernel Autoencoder (AE) model based on the idea of embedding and
reconstructing data. We argue that the classical representer theorems for
supervised kernel machines are not always applicable for (self-supervised)
representation learning, and present new representer theorems, which show that
the representations learned by our kernel models can be expressed in terms of
kernel matrices. We further derive generalisation error bounds for
representation learning with kernel SSL and AE, and empirically evaluate the
performance of these methods in both small data regimes as well as in
comparison with neural network based models.