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MiS Preprint

Discrete Restricted Boltzmann Machines

Guido Montúfar and Jason Morton


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 naive 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.

MSC Codes:
51M20, 60C05, 68Q32, 14Q15
restricted Boltzmann machine, Naive Bayes Model, Representational Power, Distributed Representation, expected dimension

Related publications

2015 Journal Open Access
Guido Montúfar and Jason Morton

Discrete restricted Boltzmann machines

In: Journal of machine learning research, 16 (2015), pp. 653-672