Walk-Sums and Belief Propagation in Gaussian Graphical Models

By Dmitry M. Malioutov, Jason K. Johnson, Alan S. Willsky. Journal of machine learning research, 2006

323 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/aa73ee74eec90b44ca0cd36607d4026b7a349469

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Citations in the corpus

Let's Make Block Coordinate Descent Go Fast: Faster Greedy Rules, Message-Passing, Active-Set Complexity, and Superlinear Convergence (2017, background): “It would also be interesting to explore whether approximate message-passing algorithms which allow general graphs [49] can be used to improve optimization algorithms.”
On Convergence Conditions of Gaussian Belief Propagation (2015, background): “It is proved in [24] that if walk-summability (or equivalently since all diagonal elements in are equal to one) is satisfied, the belief variance and belief mean can be computed with Gaussian BP under synchronous and asynchronous scheduling with message initialization and .”
Distributed Estimation of Variance in Gaussian Graphical Model via Belief Propagation: Accuracy Analysis and Improvement (2015, methodology): “In [23], using the walk-sum analysis, it is revealed that the error of BP variance is related to the summation of weights of all self-returning non-backtracking walks in the graphical model.”
Learning Latent Variable Gaussian Graphical Models (2014, background): “The precision matrix parameterization arises in many statistical inference problems for Gaussian distributions, in areas such as belief propagation (Malioutov et al., 2006), linear prediction, portfolio selection in ﬁnancial data (Ledoit & Wolf, 2003), and anomaly detection (Chen et al., 2011).”
Graphical Models, Exponential Families, and Variational Inference (2008, methodology): “3), both of which solve the quadratic program in an iterative manner, or by iterative algorithms based on tractable subgraphs [218, 158].”
Gaussian sampling by local perturbations (2010, methodology): “However, in graphs with cycles its loopy version typically underestimates the marginal variances since it overcounts the evidence, even when it converges to the correct means [13,33].”