Theory of Computing Systems (TOCS) Submission Version Finding Most Likely Solutions

As a framework for simple but basic statistical inference problems we introduce the genetic Most Likely Solution problem, the task of finding a most likely solution (MLS in short) for a given problem instance under some given probability model. Although many MLS problems are NP-hard, we propose for these problems, to study their average-case complexity under their assumed probability models. We show three examples of MLS problems, and show that “message passing algorithms” (e.g., belief propagation) work reasonably well for these problems. Some of the technical results of this paper are from the author’s recent work (Watanabe and Yamamoto in Lecture Notes in Computer Science, vol. 4142, pp. 277–282, 2006, and Onsjö and Watanabe in Lecture Notes in Computer Science, vol. 4288, pp. 507–516, 2006).

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