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Message Passing and Combinatorial Optimization Open Access


Other title
message passing
factor graph
combinatorial optimization
graphical models
survey propagation
belief propagation
loop correction
Type of item
Degree grantor
University of Alberta
Author or creator
Ravanbakhsh, Mohsen
Supervisor and department
Greiner, Russell (Computing Science)
Examining committee member and department
Moore Cristopher (Santa Fe Institute)
Szepesvari, Csaba (Computing Science)
Schuurmans, Dale (Computing Science)
Salavatipour Mohammad (Computing Science)
Department of Computing Science

Date accepted
Graduation date
Doctor of Philosophy
Degree level
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 for loopy graphs (I) loop correction techniques; (II) survey propagation, another message passing technique that surpasses BP in some settings; and (III) hybrid methods that interpolate between deterministic message passing and Markov Chain Monte Carlo inference. We then review the existing message passing solutions and provide novel graphical models and inference techniques for combinatorial problems under three broad classes: (I) constraint satisfaction problems (CSPs) such as satisfiability, coloring, packing, set / clique-cover and dominating / independent set and their optimization counterparts; (II) clustering problems such as hierarchical clustering, K-median, K-clustering, K-center and modularity optimization; (III) problems over permutations including (bottleneck) assignment, graph ``morphisms'' and alignment, finding symmetries and (bottleneck) traveling salesman problem. In many cases we show that message passing is able to find solutions that are either near optimal or favourably compare with today's state-of-the-art approaches.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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