Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
The metropolis algorithm for graph bisection
Discrete Applied Mathematics
A spectral heuristic for bisecting random graphs
Random Structures & Algorithms
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Average-case analysis for the MAX-2SAT problem
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
A simple message passing algorithm for graph partitioning problems
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Good error-correcting codes based on very sparse matrices
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
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As one simple type of statistical inference problems we consider Most Likely Solution problem, a 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 probabality models. We show three examples of MLS problems, and explain 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 joint work with his colleagues [WST, WY06, OW06] .