Quasi-free energy evaluation of Gaussian-Bernoulli restricted Boltzmann machine for anomaly detection

A Gaussian -Bernoulli restricted Boltzmann machine (GBRBM) is often used in semi -supervised anomaly detection (AD), in which the GBRBM is trained using only normal data points. The GBRBM-based AD is performed based on a score that is identical with an energy function of the marginalized GBRBM. However, it is difficult to set a threshold of the score for discriminating between a normal and an anomaly to an appropriate value because we do not equip a valid interpretation for the score value. To gain the interpretation, we focus on features of the score: the average, variance, and minimum values; and propose a sampling -based method for evaluating the features. Numerical experiments demonstrate that the proposed method can evaluate these three quantities with a high accuracy.