Discrete restricted Boltzmann machines

Guido Montúfar, Jason Morton

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naïve Bayes models. We detail the inference functions and distributed representations arising in these models in terms of configurations of projected products of simplices and normal fans of products of simplices. We bound the number of hidden variables, depending on the cardinalities of their state spaces, for which these models can approximate any probability distribution on their visible states to any given accuracy. In addition, we use algebraic methods and coding theory to compute their dimension.

Original languageEnglish (US)
Pages (from-to)653-672
Number of pages20
JournalJournal of Machine Learning Research
Volume16
StatePublished - Apr 1 2015

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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