Neighborhood-based stopping criterion for contrastive divergence

Abstract

Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence (CD) learning algorithm, an approximation to the gradient of the data log-likelihood (logL). A simple reconstruction error is often used as a stopping criterion for CD, although several authors have raised doubts concerning the feasibility of this procedure. In many cases, the evolution curve of the reconstruction error is monotonic, while the logL is not, thus indicating that the former is not a good estimator of the optimal stopping point for learning. However, not many alternatives to the reconstruction error have been discussed in the literature. An estimation of the logL of the training data based on annealed importance sampling is feasible but computationally very expensive. In this manuscript, we present a simple and cheap alternative, based on the inclusion of information contained in neighboring states to the training set, as a stopping criterion for CD learning.