Estimation in Gaussian Graphical Models Using Tractable Subgraphs: A Walk-Sum Analysis

Graphical models provide a powerful formalism for statistical signal processing. Due to their sophisticated modeling capabilities, they have found applications in a variety of fields such as computer vision, image processing, and distributed sensor networks. In this paper, we present a general class of algorithms for estimation in Gaussian graphical models with arbitrary structure. These algorithms involve a sequence of inference problems on tractable subgraphs over subsets of variables. This framework includes parallel iterations such as Embedded Trees, serial iterations such as block Gauss-Seidel, and hybrid versions of these iterations. We also discuss a method that uses local memory at each node to overcome temporary communication failures that may arise in distributed sensor network applications. We analyze these algorithms based on the recently developed walk-sum interpretation of Gaussian inference. We describe the walks "computed" by the algorithms using walk-sum dia...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: V. Chandrasekaran, Jason K. Johnson, Alan S. Willsky
• Keywords: Algorithms, Graphical Models, Iterations, TSP 2008