Boltzmann Machines with Bounded Continuous Random Variables

Abstract

We propose a Boltzmann machine formulated as a probabilistic model where every random variable takes bounded continuous values, and we derive the Thouless–Anderson–Palmer equation for the model. The proposed model includes the non-negative Boltzmann machine and the Sherrington–Kirkpatrick model with spin-S at S→∞ as a special case. It is known that the Sherrington–Kirkpatrick model with spin-S has a spin glass phase. Thus, the proposed Boltzmann machine is expected to be able to learn practical complex data.