Asymptotic Normality of the Maximum Pseudolikelihood Estimator for Fully Visible Boltzmann Machines

Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood estimation (MPLE) results in parameter estimates which are consistent in the probabilistic sense. In this article, we investigate the properties of MPLE for the fully visible BMs further, and prove that MPLE also yields an asymptotically normal parameter estimator. These results can be used to construct confidence intervals and to test statistical hypotheses. We support our theoretical results by showing that the estimator behaves as expected in a simulation study

Contrastive Learning for Lifted Networks

In this work we address supervised learning of neural networks via lifted network formulations. Lifted networks are interesting because they allow training on massively parallel hardware and assign energy models to discriminatively trained neural networks. We demonstrate that the training methods for lifted networks proposed in the literature have significant limitations and show how to use a contrastive loss to address those limitations. We demonstrate that this contrastive training approximates back-propagation in theory and in practice and that it is superior to the training objective regularly used for lifted networks.Comment: 9 pages, BMVC 201