Approximate inference for robust Gaussian process regression
Malte Kuß, Tobias Pfingsten, Lehel Csató, Carl Edward Rasmussen · Cambridge University Engineering Department Publications Database · 2005
Abstract. Gaussian process (GP) priors have been successfully used in non-parametric Bayesian regression and classification models. Inference can be performed analytically only for the regression model with Gaussian noise. For all other likelihood models inference is intractable and various approximation techniques have been proposed. In recent years expectation-propagation (EP) has been developed as a general method for approximate inference. This article provides a general summary of how expectationpropagation can be used for approximate inference in Gaussian process models. Furthermore we present a case study describing its implementation for a new robust variant of Gaussian process regression. To gain further insights into the quality of the EP approximation we present experiments in which we compare to results obtained by Markov chain Monte Carlo (MCMC) sampling. 1 Introduction – Robustness & Bayesian Regression To solve a real-world regression problem the analyst should carefully screen the data and use all prior information at hand in order to choose an appropriate regression model. The model is selected so as to approximate the beliefs about the data generating process. A mismatch seems unavoidable in practice. Robust regression methods can be understood as attempts to limit undesired distractions and distortions