A Closed-Form Estimator of Fully Visible Boltzmann Machines

Several researchers have recently proposed alternative estimatiou methods of Boltzmann machines (BMs) beyond the standard maximum likelihood framework. Examples are the coutrastive divergence or the ratio matching, and also a rather classic pseudolikelihood method. With a loss of statistical efficiency, alternative methods can often speedup the computation and/or simplify the, implementation. In this article, as an extreme of this direction, we show the parameter estimation of BMs can be done even with a closed-form estimator, by recasting the problem into linear regression. We confirm our estimator can actually approach the true parameter as the sample size increases, while the convergence can be slow, by a simple simulation experiment.