Boltzmann machines and energy-based models

We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log likelihood of data is increased. The gradient and Hessian of a Boltzmann machine admit beautiful mathematical representations, although computing them is in general intractable. This intractability motivates approximate methods, including Gibbs sampler and contrastive divergence, and tractable alternatives, namely energy-based models.