Efficient Learning of Restricted Boltzmann Machines Using Covariance Estimates
This work addresses the computational bottleneck in training RBMs for researchers and practitioners, though it is incremental as it builds on existing gradient descent and Hessian approximation techniques.
The paper tackles the problem of inefficient learning in Restricted Boltzmann Machines (RBMs) by proposing an algorithm that uses the inverse of a diagonal approximation of the Hessian, derived from covariance estimates, to set adaptive learning rates, resulting in more efficient learning compared to standard methods.
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.