Abstract
In this paper, which is based on the important recent work of Yedidia, Freeman, and Weiss, we present a generalized form of belief propagation, viz. belief propagation on a partially ordered set (PBP). PBP is an iterative message-passing algorithm for solving, either exactly or approximately, the marginalized product density problem, which is a general computational problem of wide applicability. We will show that PBP can be thought of as an algorithm for minimizing a certain “free energy” function, and by exploiting this interpretation, we will exhibit a one-to-one correspondence between the fixed points of PBP and the stationary points of the free energy.
This research was supported by NSF grant no. CCR-0118670, and grants from Sony, Qualcomm. and Caltech’s Lee Center for Advanced Networking.
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McEliece, R.J., Yildirim, M. (2003). Belief Propagation on Partially Ordered Sets. In: Rosenthal, J., Gilliam, D.S. (eds) Mathematical Systems Theory in Biology, Communications, Computation, and Finance. The IMA Volumes in Mathematics and its Applications, vol 134. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21696-6_10
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DOI: https://doi.org/10.1007/978-0-387-21696-6_10
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