Sampling the Riemann-Theta Boltzmann Machine

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.