Discovering Hidden Features with Gaussian Processes Regression

Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)

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Francesco Vivarelli, Christopher Williams


We study the dynamics of supervised learning in layered neural net(cid:173) works, in the regime where the size p of the training set is proportional to the number N of inputs. Here the local fields are no longer described by Gaussian distributions. We use dynamical replica theory to predict the evolution of macroscopic observables, including the relevant error measures, incorporating the old formalism in the limit piN --t 00.