What cannot be learned with bethe approximations

Uri Heinemann, Amir Globerson

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

Abstract

We address the problem of learning the parameters in graphical models when inference is intractable. A common strategy in this case is to replace the partition function with its Bethe approximation. We show that there exists a regime of empirical marginals where such Bethe learning will fail. By failure we mean that the empirical marginals cannot be recovered from the approximated maximum likelihood parameters (i.e., moment matching is not achieved). We provide several conditions on empirical marginals that yield outer and inner bounds on the set of Bethe learnable marginals. An interesting implication of our results is that there exists a large class of marginals that cannot be obtained as stable fixed points of belief propagation. Taken together our results provide a novel approach to analyzing learning with Bethe approximations and highlight when it can be expected to work or fail.

Original languageEnglish
Title of host publicationProceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011
PublisherAUAI Press
Pages319-326
Number of pages8
StatePublished - 2011
Externally publishedYes

Publication series

NameProceedings of the 27th Conference on Uncertainty in Artificial Intelligence, UAI 2011

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