Walk-Sum Interpretation and Analysis of Gaussian Belief Propagation
Abstract
This paper presents a new framework based on walks in a graph for analysis and inference in Gaussian graphical models. The key idea is to decompose correlations between variables as a sum over all walks between those variables in the graph. The weight of each walk is given by a product of edgewise partial correlations. We provide a walk-sum interpretation of Gaussian belief propagation in trees and of the approximate method of loopy belief propagation in graphs with cycles. This perspective leads to a better understanding of Gaussian belief propagation and of its convergence in loopy graphs.
Cite
Text
Malioutov et al. "Walk-Sum Interpretation and Analysis of Gaussian Belief Propagation." Neural Information Processing Systems, 2005.Markdown
[Malioutov et al. "Walk-Sum Interpretation and Analysis of Gaussian Belief Propagation." Neural Information Processing Systems, 2005.](https://mlanthology.org/neurips/2005/malioutov2005neurips-walksum/)BibTeX
@inproceedings{malioutov2005neurips-walksum,
title = {{Walk-Sum Interpretation and Analysis of Gaussian Belief Propagation}},
author = {Malioutov, Dmitry and Willsky, Alan S. and Johnson, Jason K.},
booktitle = {Neural Information Processing Systems},
year = {2005},
pages = {579-586},
url = {https://mlanthology.org/neurips/2005/malioutov2005neurips-walksum/}
}