Sampling the Riemann-Theta Boltzmann Machine
This provides a method for sampling in a specific machine learning model, which is incremental as it builds on existing Boltzmann machine theory.
The paper tackled the problem of sampling from the visible sector probability density function of the Riemann-Theta Boltzmann machine by showing it corresponds to an infinite Gaussian mixture model, enabling straightforward sampling and revealing an affine transform property.
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.