Sampling the Riemann-Theta Boltzmann Machine

TL;DR

This paper demonstrates that the Riemann-Theta Boltzmann machine's visible probability density can be viewed as an infinite Gaussian mixture, enabling straightforward sampling and revealing affine transform properties similar to Gaussian densities.

Contribution

It introduces a novel interpretation of the Riemann-Theta Boltzmann machine's density as an infinite Gaussian mixture, facilitating sampling and analysis.

Findings

The visible density is an infinite Gaussian mixture.

Sampling can be performed straightforwardly.

The density has an affine transform property.

Abstract

We show that the visible sector probability density function of the Riemann-Theta Boltzmann machine corresponds to a gaussian mixture model consisting of an infinite number of component multi-variate gaussians. The weights of the mixture are given by a discrete multi-variate gaussian over the hidden state space. This allows us to sample the visible sector density function in a straight-forward manner. Furthermore, we show that the visible sector probability density function possesses an affine transform property, similar to the multi-variate gaussian density.