Gaussian Processes for Bayesian Classification via Hybrid Monte Carlo

The full Bayesian method for applying neural networks to a prediction problemis to set up the prior/hyperprior structure for the net and then perform the necessary integrals. However, these integrals arenot tractable analytically, and Markov Chain Monte Carlo (MCMC) methods are slow, especially if the parameter space is high-dimensional. Using Gaussian processes we can approximate the weight space integral analytically, so that only a small number of hyperparameters need be integrated over by MCMC methods. We have applied this idea to classification problems, obtaining excellent resultson the real-world problems investigated so far. 1 INTRODUCTION To make predictions based on a set of training data, fundamentally we need to combine our prior beliefs about possible predictive functions with the data at hand. In the Bayesian approach to neural networks a prior on the weights in the net induces a prior distribution over functions.