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Learning RBMs using standard algorithms such as CD(k) involves gradientdescent on the negative log-likelihood. One of the terms in the gradient, whichinvolves expectation w.r.t. the model distribution, is intractable and isobtained through an MCMC estimate. In this work we show that the Hessian of thelog-likelihood can be written in terms of covariances of hidden and visibleunits and hence, all elements of the Hessian can also be estimated using thesame MCMC samples with small extra computational costs. Since inverting theHessian may be computationally expensive, we propose an algorithm that usesinverse of the diagonal approximation of the Hessian, instead. This essentiallyresults in parameter-specific adaptive learning rates for the gradient descentprocess and improves the efficiency of learning RBMs compared to the standardmethods. Specifically we show that using the inverse of diagonal approximationof Hessian in the stochastic DC (difference of convex functions) programapproach results in very efficient learning of RBMs.

Efficient Learning of Restricted Boltzmann Machines Using Covariance Estimates