Minimization of continuous bethe approximations: A positive variation

Jason L. Pacheco, Erik B. Sudderth

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We develop convergent minimization algorithms for Bethe variational approximations which explicitly constrain marginal estimates to families of valid distributions. While existing message passing algorithms define fixed point iterations corresponding to stationary points of the Bethe free energy, their greedy dynamics do not distinguish between local minima and maxima, and can fail to converge. For continuous estimation problems, this instability is linked to the creation of invalid marginal estimates, such as Gaussians with negative variance. Conversely, our approach leverages multiplier methods with well-understood convergence properties, and uses bound projection methods to ensure that marginal approximations are valid at all iterations. We derive general algorithms for discrete and Gaussian pairwise Markov random fields, showing improvements over standard loopy belief propagation. We also apply our method to a hybrid model with both discrete and continuous variables, showing improvements over expectation propagation.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 25
Subtitle of host publication26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Pages2564-2572
Number of pages9
StatePublished - 2012
Externally publishedYes
Event26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States
Duration: Dec 3 2012Dec 6 2012

Publication series

NameAdvances in Neural Information Processing Systems
Volume4
ISSN (Print)1049-5258

Other

Other26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012
Country/TerritoryUnited States
CityLake Tahoe, NV
Period12/3/1212/6/12

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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