Efficient Approaches to Gaussian Process Classification
Lehel Csató, Ernest Fokoué, Manfred Opper, Bernhard Schottky, Ole Winther · 1999
We present three simple approximations for the calculation of the posterior mean in Gaussian Process classification. The first two methods are related to mean field ideas known in Statistical Physics. The third approach is based on Bayesian online approach which was motivated by recent results in the Statistical Mechanics of Neural Networks. We present simulation results showing: 1. that the mean field Bayesian evidence may be used for hyperparameter tuning and 2. that the online approach may achieve a low training error fast. 1 Introduction Gaussian processes provide promising non-parametric Bayesian approaches to regression and classification [2, 1]. In these statistical models, it is assumed that the likelihood of an output or target variable y for a given input x 2 R N can be written as P (yja(x)) where a : R N ! R are functions which have a Gaussian prior distribution, i.e. a is (a priori) assumed to be a Gaussian random field. This means that any finite set of field...