Universal Approximation Results for the Temporal Restricted Boltzmann Machine and the Recurrent Temporal Restricted Boltzmann Machine

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dc.contributor.authorOdense, Simon
dc.contributor.authorEdwards, Roderick
dc.date.accessioned2021-07-26T22:16:54Z
dc.date.available2021-07-26T22:16:54Z
dc.date.copyright2016en_US
dc.date.issued2016
dc.description.abstractThe Restricted Boltzmann Machine (RBM) has proved to be a powerful tool in machine learning, both on its own and as the building block for Deep Belief Networks (multi-layer generative graphical models). The RBM and Deep Belief Network have been shown to be universal approximators for probability distributions on binary vectors. In this paper we prove several similar universal approximation results for two variations of the Restricted Boltzmann Machine with time dependence, the Temporal Restricted Boltzmann Machine (TRBM) and the Recurrent Temporal Restricted Boltzmann Machine (RTRBM). We show that the TRBM is a universal approximator for Markov chains and generalize the theorem to sequences with longer time dependence. We then prove that the RTRBM is a universal approximator for stochastic processes with nite time dependence. We conclude with a discussion on e ciency and how the constructions developed could explain some previous experimental results.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipThe authors thank NSERC and the University of Victoria for partial funding of this work.en_US
dc.identifier.citationOdense, S. & Edwards, R. (2016). Universal approximation results for the temporal restricted Boltzmann machine the recurrent temporal restricted Boltzmann machine. Journal of Machine Learning Research, 17(158), 1-21. http://jmlr.org/papers/v17/15-478.htmlen_US
dc.identifier.otherhttp://jmlr.org/papers/v17/15-478.html
dc.identifier.urihttp://hdl.handle.net/1828/13176
dc.language.isoenen_US
dc.publisherJournal of Machine Learning Researchen_US
dc.subjectTRBM
dc.subjectRTRBM
dc.subjectmachine learning
dc.subjectuniversal approximation
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleUniversal Approximation Results for the Temporal Restricted Boltzmann Machine and the Recurrent Temporal Restricted Boltzmann Machineen_US
dc.typeArticleen_US

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