Reducing the Complexity of Graphical Models via Cycles

SPEAKER: Mr. Thomas R. Halford, Communication Sciences Institute, University of Southern CaliforniaABSTRACT: A decade ago, the introduction of turbo codes and iterative message passing algorithms revolutionized the theory and practice of coding. In the ensuing years, the coding theory community has become adept at designing codes from good graphical models - that is, models which imply low-complexity, near-optimal iterative message passing algorithms. Specifically, modern codes are constructed by connecting a large number of simple local codes together via a rich, random-like, cyclic interconnection network. A key observation from this work is that the introduction of cycles to graphical models can enable massive complexity reductions in model, and thus decoding, complexity.Whereas constructive graphical modeling problems (e.g. code design) have been widely addressed by the coding theory community, less is understood about the inverse problem of model extraction. Specifically, can good graphical models be obtained for existing algebraic codes, or more generally, for arbitrary systems? What tradeoffs exist between model complexity and cyclic topology for a given code? If good models can exist, how can they be obtained, or extracted? This talk presents a theoretical framework for the study of extractive graphical modeling problems. We first examine the limits of extraction by providing a characterization of the tradeoff between cyclic topology and complexity in graphical models for linear codes. Inasmuch as the cyclic topology of a graphical model is related to the performance of the decoding algorithms it implies, the bound presented in this talk provides insight into the limits of graphical model extraction. We then provide a formalization of extraction as optimization and describe some novel heuristics for both defining and solving this optimization problem. We conclude with a discussion of the importance of cyclic model extraction outside of coding.Bio: Thomas R. Halford received the B. A. Sc. degree in engineering physics from Simon Fraser University, Burnaby, B.C., Canada, in 2001. He is currently a doctoral candidate at the University of Southern California, Los Angeles, where his research focuses primarily on graphical models of codes. He spent the summer of 2005 visiting the Natural Language Processing Group at IBM T. J. Watson Research Center, Yorktown Heights, NY.Host: Prof. Keith M. Chugg, chugg@usc.edu

Location: Hughes Aircraft Electrical Engineering Center (EEB) - 248

Audiences: Everyone Is Invited

Contact: Mayumi Thrasher