  A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined
on a bipartite graph and is an extension of usual restricted Boltzmann
machines. A GRBM consists of two different layers: a visible layer composed of
continuous visible variables and a hidden layer composed of discrete hidden
variables. In this paper, we derive two different inference algorithms for
GRBMs based on the naive mean-field approximation (NMFA). One is an inference
algorithm for whole variables in a GRBM, and the other is an inference
algorithm for partial variables in a GBRBM. We compare the two methods
analytically and numerically and show that the latter method is better.
