A Unified Framework for Closed-Form Nonparametric Regression, Classification, Preference and Mixed Problems with Skew Gaussian Processes

Abstract

Gaussian Processes (GPs) are powerful nonparametric distributions over functions. For real-valued outputs, we can combine the GP prior with a Gaussian likelihood and perform exact posterior inference in closed form. However, in other cases, such as classification, preference learning, ordinal regression and mixed problems, the likelihood is no longer conjugate to the GP prior and a closed-form expression for the posterior is not available.