Learning multi-linear representations of distributions for efficient inference

Dan Roth, Rajhans Samdani

Research output: Contribution to journalArticlepeer-review


We examine the class of multi-linear representations (MLR) for expressing probability distributions over discrete variables. Recently, MLR have been considered as intermediate representations that facilitate inference in distributions represented as graphical models. We show that MLR is an expressive representation of discrete distributions and can be used to concisely represent classes of distributions which have exponential size in other commonly used representations, while supporting probabilistic inference in time linear in the size of the representation. Our key contribution is presenting techniques for learning bounded-size distributions represented using MLR, which support efficient probabilistic inference. We demonstrate experimentally that the MLR representations we learn support accurate and very efficient inference.

Original languageEnglish (US)
Pages (from-to)195-209
Number of pages15
JournalMachine Learning
Issue number2-3
StatePublished - Sep 2009
Externally publishedYes


  • Graphical models
  • Learning probability distributions
  • Multi-linear polynomials
  • Probabilistic inference

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence


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