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Geometry and expressive power of conditional restricted Boltzmann machines
Publikationstyp
Journal Article
Date Issued
2015-12-15
Sprache
English
Author(s)
Volume
16
Start Page
2405
End Page
2436
Citation
Journal of Machine Learning Research 16: 2405-2436 (2015-12-)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Microtome Publishing
Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parameterized by interaction weights and biases. We address the representational power of these models, proving results on their ability to represent conditional Markov random fields and conditional distributions with restricted supports, the minimal size of universal approximators, the maximal model approximation errors, and on the dimension of the set of representable conditional distributions. We contribute new tools for investigating conditional probability models, which allow us to improve the results that can be derived from existing work on restricted Boltzmann machine probability models.
Subjects
Conditional restricted Boltzmann machine
Expected dimension
Kullback-Leibler approximation error
Universal approximation
DDC Class
510: Mathematik
600: Technik