  Learning RBMs using standard algorithms such as CD(k) involves gradient
descent on the negative log-likelihood. One of the terms in the gradient, which
involves expectation w.r.t. the model distribution, is intractable and is
obtained through an MCMC estimate. In this work we show that the Hessian of the
log-likelihood can be written in terms of covariances of hidden and visible
units and hence, all elements of the Hessian can also be estimated using the
same MCMC samples with small extra computational costs. Since inverting the
Hessian may be computationally expensive, we propose an algorithm that uses
inverse of the diagonal approximation of the Hessian, instead. This essentially
results in parameter-specific adaptive learning rates for the gradient descent
process and improves the efficiency of learning RBMs compared to the standard
methods. Specifically we show that using the inverse of diagonal approximation
of Hessian in the stochastic DC (difference of convex functions) program
approach results in very efficient learning of RBMs.
