Sampling the Riemann-theta Boltzmann machine. (English) Zbl 1525.62020
Summary: 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 straightforward manner. Furthermore, we show that the visible sector probability density function possesses an affine transform property, similar to the multi-variate Gaussian density.
MSC:
| 62G07 | Density estimation |
| 60-08 | Computational methods for problems pertaining to probability theory |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 68T07 | Artificial neural networks and deep learning |
Software:
GitHubReferences:
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