Orbit-product representation and correction of Gaussian belief propagation

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We present a new interpretation of Gaussian belief propagation (GaBP) based on the 'zeta function' representation of the determinant as a product over orbits of a graph. We show that GaBP captures back-tracking orbits of the graph and consider how to correct this estimate by accounting for non-backtracking orbits. We show that the product over non-backtracking orbits may be interpreted as the determinant of the non-backtracking adjacency matrix of the graph with edge weights based on the solution of GaBP. An efficient method is proposed to compute a truncated correction factor including all non-backtracking orbits up to a specified length.

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Johnson, Jason K; Chertkov, Michael & Chernyak, Vladimir January 1, 2009.

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We present a new interpretation of Gaussian belief propagation (GaBP) based on the 'zeta function' representation of the determinant as a product over orbits of a graph. We show that GaBP captures back-tracking orbits of the graph and consider how to correct this estimate by accounting for non-backtracking orbits. We show that the product over non-backtracking orbits may be interpreted as the determinant of the non-backtracking adjacency matrix of the graph with edge weights based on the solution of GaBP. An efficient method is proposed to compute a truncated correction factor including all non-backtracking orbits up to a specified length.

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  • Inter. Conference Machine Learning ; June 14, 2009 ; Montreal, Canada

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  • Report No.: LA-UR-09-00745
  • Report No.: LA-UR-09-745
  • Grant Number: AC52-06NA25396
  • Office of Scientific & Technical Information Report Number: 956389
  • Archival Resource Key: ark:/67531/metadc933486

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  • January 1, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 12, 2016, 12:38 p.m.

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Johnson, Jason K; Chertkov, Michael & Chernyak, Vladimir. Orbit-product representation and correction of Gaussian belief propagation, article, January 1, 2009; [New Mexico]. (digital.library.unt.edu/ark:/67531/metadc933486/: accessed December 11, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.