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MiS Preprint
87/2018
Restricted Boltzmann Machines: Introduction and Review
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Boltzmann machines carry a rich structure, with connections to geometry, applied algebra, probability, statistics, machine learning, and other areas. The analysis of these models is attractive in its own right and also as a platform to combine and generalize mathematical tools for graphical models with hidden variables. This article gives an introduction to the mathematical analysis of restricted Boltzmann machines, reviews recent results on the geometry of the sets of probability distributions representable by these models, and suggests a few directions for further investigation.
In: International conference on information geometry and its applications IV : Liblice, June 12-17, 2016 ; in honor of Shun-ichi Amari / Nihat Ay... (eds.) Praha : Matfyzpress, 2016. - pp. 25-25
Restricted Boltzmann machines : introduction and review
In: Information geometry and its applications : on the occasion of Shun-ichi Amari's 80th Birthday, IGAIA IV Liblice, Czech Republic, June 2016 / Nihat Ay... (eds.) Cham : Springer, 2018. - pp. 75-115 (Springer proceedings in mathematics and statistics ; 252)
