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...

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Detalles Bibliográficos
Autores principales: Carrazza, Stefano, Krefl, Daniel
Lenguaje:eng
Publicado: 2018
Materias:
stat.ML
cs.LG
Computing and Computers
Other
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1016/j.cpc.2020.107464
http://cds.cern.ch/record/2639022
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author Carrazza, Stefano
Krefl, Daniel
author_facet Carrazza, Stefano
Krefl, Daniel
author_sort Carrazza, Stefano
collection CERN
description 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.
id oai-inspirehep.net-1694236
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2018
record_format invenio
spelling oai-inspirehep.net-16942362023-10-04T06:33:26Zdoi:10.1016/j.cpc.2020.107464http://cds.cern.ch/record/2639022engCarrazza, StefanoKrefl, DanielSampling the Riemann-Theta Boltzmann Machinestat.MLcs.LGComputing and ComputersOtherComputing and ComputersMathematical Physics and MathematicsWe 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.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.arXiv:1804.07768CERN-TH-2018-085CERN-TH-2018-085oai:inspirehep.net:16942362018-04-20
spellingShingle stat.ML
cs.LG
Computing and Computers
Other
Computing and Computers
Mathematical Physics and Mathematics
Carrazza, Stefano
Krefl, Daniel
Sampling the Riemann-Theta Boltzmann Machine
title Sampling the Riemann-Theta Boltzmann Machine
title_full Sampling the Riemann-Theta Boltzmann Machine
title_fullStr Sampling the Riemann-Theta Boltzmann Machine
title_full_unstemmed Sampling the Riemann-Theta Boltzmann Machine
title_short Sampling the Riemann-Theta Boltzmann Machine
title_sort sampling the riemann-theta boltzmann machine
topic stat.ML
cs.LG
Computing and Computers
Other
Computing and Computers
Mathematical Physics and Mathematics
url https://dx.doi.org/10.1016/j.cpc.2020.107464
http://cds.cern.ch/record/2639022
work_keys_str_mv AT carrazzastefano samplingtheriemannthetaboltzmannmachine
AT krefldaniel samplingtheriemannthetaboltzmannmachine

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