Belief propagation: accurate marginals or accurate partition function—where is the difference?

Christian Knoll*, Franz Pernkopf

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We analyze belief propagation on patch potential models—attractive models with varying local potentials—obtain all of the potentially many fixed points, and gather novel insights into belief propagation properties. In particular, we observe and theoretically explain several regions in the parameter space that behave fundamentally differently. We specify and elaborate on one specific region that, despite the existence of multiple fixed points, is relatively well behaved and provides insights into the relationship between the accuracy of the marginals and the partition function. We demonstrate the inexistence of a principal relationship between both quantities and provide sufficient conditions for a fixed point to be optimal with respect to approximating both the marginals and the partition function.
Original languageEnglish
Article number124009
JournalJournal of Statistical Mechanics: Theory and Experiment
Volume2020
Issue number12
DOIs
Publication statusPublished - 21 Dec 2020

Keywords

  • machine learning

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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