Mean Field Methods for Classification with Gaussian Processes

We discuss the application of TAP mean field methods known from the Statistical Mechanics of disordered systems to Bayesian classifi(cid:173) cation models with Gaussian processes. In contrast to previous ap(cid:173) proaches, no knowledge about the distribution of inputs is needed. Simulation results for the Sonar data set are given. Bayesian models which are based on Gaussian prior distributions on function spaces are promising non-parametric statistical tools. They have been recently introduced into the Neural Computation community (Neal 1996, Williams & Rasmussen 1996, Mackay 1997).