In this talk, we consider a weighted complete bipartite graph and
define a probability distribution on it whose MAP assignment corresponds to the maximum
weight matching (MWM) in that graph. We analyze the fixed points of the max-product
algorithm when run on this graph and prove that even though the underlying graph has
many (short) cycles, the max-product assignment converges to the correct MAP assignment.
Finally, we will identify a large class of optimization problems for which the
fixed points of max-product algorithm are solutions of the optimization problems.
This talk is based on a joint work with Mohsen Bayati and Mayank Sharma at Stanford
University.

Keywords:

Phase Transition;Computation;Reconstruction

Lecture #10873

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