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.

中文翻译：

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采样 Riemann-Theta Boltzmann 机

我们表明，黎曼-Theta Boltzmann 机的可见扇区概率密度函数对应于由无限多个分量多变量高斯组成的高斯混合模型。混合的权重由隐藏状态空间上的离散多变量高斯给出。这使我们能够以直接的方式对可见扇区密度函数进行采样。此外，我们表明可见扇区概率密度函数具有仿射变换特性，类似于多元高斯密度。