On Theoretical Properties of Sum-Product Networks

On Theoretical Properties of Sum-Product Networks

Abstract

Sum-product networks (SPNs) are a promis-ing avenue for probabilistic modeling andhave been successfully applied to varioustasks. However, some theoretic propertiesabout SPNs are not yet well understood. Inthis paper we fill some gaps in the theoreticfoundation of SPNs. First, we show that theweights of any complete and consistent SPNcan be transformed into locally normalizedweights without changing the SPN distribu-tion. Second, we show that consistent SPNscannot model distributions significantly (ex-ponentially) more compactly than decompos-able SPNs. As a third contribution, we ex-tend the inference mechanisms known forSPNs with finite states to generalized SPNswith arbitrary input distributions.

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Authors
  • Peharz, Robert
  • Tschiatschek, Sebastian
  • Pernkopf, Franz
  • Domingos, Pedro M.
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Shortfacts
Category
Paper in Conference Proceedings or in Workshop Proceedings (Paper)
Event Title
International Conference on Artificial Intelligence and Statistics (AISTATS)
Divisions
Data Mining and Machine Learning
Event Location
San Diego, California, USA
Event Type
Conference
Event Dates
09.-12.05.2015
Series Name
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38
Page Range
pp. 744-752
Date
9 May 2015
Official URL
https://www.tschiatschek.net/files/peharz15theoret...
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