Variable sigma Gaussian processes: An expectation propagation perspective

TL;DR

This paper extends variable-sigma Gaussian processes to classification and other tasks by deriving them via expectation propagation, allowing each basis point to have its own covariance, thus improving approximation accuracy.

Contribution

The paper introduces a new perspective on variable-sigma GPs using expectation propagation, enabling their application beyond regression and enhancing their flexibility.

Findings

VSGP can be effectively applied to classification problems.

Allowing basis points to have full covariance matrices improves approximation accuracy.

The expectation propagation framework unifies and extends sparse GP methods.

Abstract

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate GP methods have been proposed that essentially map the large dataset into a small set of basis points. The most advanced of these, the variable-sigma GP (VSGP) (Walder et al., 2008), allows each basis point to have its own length scale. However, VSGP was only derived for regression. We describe how VSGP can be applied to classification and other problems, by deriving it as an expectation propagation algorithm. In this view, sparse GP approximations correspond to a KL-projection of the true posterior onto a compact exponential family of GPs. VSGP constitutes one such family, and we show how to enlarge this family to get additional accuracy. In particular, we show that endowing each basis point with its own full covariance matrix provides a significant increase in approximation power.