# Sampling the Riemann-Theta Boltzmann Machine

arXiv: https://arxiv.org/abs/1804.07768 · HTML: https://mlsanity.com/paper/1804.07768/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Product Jacobi-Theta Boltzmann machines with score matching](https://mlsanity.com/paper/2303.05910/) (2023)

## Abstract (arXiv)

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.