Skew Gaussian Processes for Classification

TL;DR

This paper introduces Skew-Gaussian processes (SkewGPs), a flexible nonparametric Bayesian model that captures asymmetry in data, extending Gaussian processes for improved classification performance.

Contribution

The paper proposes SkewGPs, extending Gaussian processes with skewness, and derives closed-form expressions for classification, demonstrating improved empirical results over traditional GPs.

Findings

SkewGP classifier outperforms GP classifiers with Laplace and Expectation Propagation.

Closed-form expressions for marginal likelihood and predictive distribution are derived.

SkewGPs effectively model asymmetric data distributions.

Abstract

Gaussian processes (GPs) are distributions over functions, which provide a Bayesian nonparametric approach to regression and classification. In spite of their success, GPs have limited use in some applications, for example, in some cases a symmetric distribution with respect to its mean is an unreasonable model. This implies, for instance, that the mean and the median coincide, while the mean and median in an asymmetric (skewed) distribution can be different numbers. In this paper, we propose Skew-Gaussian processes (SkewGPs) as a non-parametric prior over functions. A SkewGP extends the multivariate Unified Skew-Normal distribution over finite dimensional vectors to a stochastic processes. The SkewGP class of distributions includes GPs and, therefore, SkewGPs inherit all good properties of GPs and increase their flexibility by allowing asymmetry in the probabilistic model. By exploiting the fact that SkewGP and probit likelihood are conjugate model, we derive closed form expressions for the marginal likelihood and predictive distribution of this new nonparametric classifier. We verify empirically that the proposed SkewGP classifier provides a better performance than a GP classifier based on either Laplace's method or Expectation Propagation.