Combinatorial Markov random fields

Ron Bekkerman, Mehran Sahami, Erik Learned-Miller

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A combinatorial random variable is a discrete random variable defined over a combinatorial set (e.g., a power set of a given set). In this paper we introduce combinatorial Markov random fields (Comrafs), which are Markov random fields where some of the nodes are combinatorial random variables. We argue that Comrafs are powerful models for unsupervised and semi-supervised learning. We put Comrafs in perspective by showing their relationship with several existing models. Since it can be problematic to apply existing inference techniques for graphical models to Comrafs, we design two simple and efficient inference algorithms specific for Comrafs, which are based on combinatorial optimization. We show that even such simple algorithms consistently and significantly outperform Latent Dirichlet Allocation (LDA) on a document clustering task. We then present Comraf models for semi-supervised clustering and transfer learning that demonstrate superior results in comparison to an existing semi-supervised scheme (constrained optimization).

Original languageEnglish
Title of host publicationMachine Learning
Subtitle of host publicationECML 2006 - 17th European Conference on Machine Learning, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)354045375X, 9783540453758
StatePublished - 2006
Externally publishedYes
Event17th European Conference on Machine Learning, ECML 2006 - Berlin, Germany
Duration: 18 Sep 200622 Sep 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4212 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th European Conference on Machine Learning, ECML 2006

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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