Abstract
A Boltzmann machine is known as a stochastically exteded model of the Hopfield neural network. It is not only a neural network model but related to various fields, such as statistics, statistical mechanics, information geometry, and so on. We review various aspects of a Boltzmann machine such as dynamics, learning rule, maximum entropy property, spatial Markovian property, and so on, in view of the general theories of Gibbs sampler, expontial family and Markov random field. Some recent studies on the application of Boltzmann machines are also reviewed.
