Bayesian Training of Backpropagation Networks by the Hybrid Monte Carlo Method

. It is shown that Bayesian training of backpropagation neural networks can feasibly be performed by the "Hybrid Monte Carlo" method. This approach allows the true predictive distribution for a test case given a set of training cases to be approximated arbitrarily closely, in contrast to previous approaches which approximate the posterior weight distribution by a Gaussian. In this work, the Hybrid Monte Carlo method is implemented in conjunction with simulated annealing, in order to speed relaxation to a good region of parameter space. The method has been applied to a test problem, demonstrating that it can produce good predictions, as well as an indication of the uncertainty of these predictions. Appropriate weight scaling factors are found automatically. By applying known techniques for calculation of "free energy" differences, it should also be possible to compare the merits of different network architectures. The work described here should also be applicable to a wide variety of st..