Approximate Inference on Planar Graphs using Loop Calculus and Belief Propagation

  • Gómez V
  • Kappen B
  • 42

    Readers

    Mendeley users who have this article in their library.
  • 0

    Citations

    Citations of this article.

Abstract

We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006a) allows to express the exact partition function of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in Chertkov et al. (2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze the performance of the algorithm for models with binary variables and pairwise interactions on grids and other planar graphs. We study in detail both the loop series and the equivalent Pfaffian series and show that the first term of the Pfaffian series for the general, intractable planar model, can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state of the art methods for approximate inference. Keywords: belief propagation, loop calculus, approximate inference, partition function, planar graphs, Ising model

Author-supplied keywords

  • computational
  • information theoretic learning with statistics
  • learning
  • statistics & optimisation

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Vicenc¸ Gómez

  • Bert Kappen

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free