Message Passing and Combinatorial Optimization
Siamak Ravanbakhsh

TL;DR
This paper explores message passing algorithms for graphical models, focusing on improving inference techniques for complex combinatorial problems and demonstrating their near-optimal solutions across various problem classes.
Contribution
It introduces novel message passing methods, including loop corrections and hybrid approaches, to enhance inference in loopy graphs and applies these to diverse combinatorial problems.
Findings
Message passing can find near-optimal solutions for complex combinatorial problems.
Loop correction techniques improve Belief Propagation accuracy.
Hybrid methods outperform traditional approaches in certain settings.
Abstract
Graphical models use the intuitive and well-studied methods of graph theory to implicitly represent dependencies between variables in large systems. They can model the global behaviour of a complex system by specifying only local factors. This thesis studies inference in discrete graphical models from an algebraic perspective and the ways inference can be used to express and approximate NP-hard combinatorial problems. We investigate the complexity and reducibility of various inference problems, in part by organizing them in an inference hierarchy. We then investigate tractable approximations for a subset of these problems using distributive law in the form of message passing. The quality of the resulting message passing procedure, called Belief Propagation (BP), depends on the influence of loops in the graphical model. We contribute to three classes of approximations that improve BP…
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Taxonomy
Topicsgraph theory and CDMA systems · Cognitive Computing and Networks · Computability, Logic, AI Algorithms
