Learning and Evaluating Boltzmann Machines

We provide a brief overview of the variational framework for obtaining deterministic approximations or upper bounds for the log-partition function. We also review some of the Monte Carlo based methods for estimating partition functions of arbitrary Markov Random Fields. We then develop an annealed importance sampling (AIS) procedure for estimating partition functions of restricted Boltzmann machines (RBM’s), semi-restricted Boltzmann machines (SRBM’s), and Boltzmann machines (BM’s). Our empirical results indicate that the AIS procedure provides much better estimates of the partition function than some of the popular variational-based methods. Finally, we develop a new learning algorithm for training general Boltzmann machines and show that it can be successfully applied to learning good generative models. Learning and Evaluating Boltzmann Machines Ruslan Salakhutdinov Department of Computer Science, University of Toronto