Belief Propagation and Revision in Networks with Loops (1997) [52 citations — 5 self]
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http://www-bcs.mit.edu/people/yweiss/cbcl.ps.gz
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author = {Yair Weiss},
title = {Belief Propagation and Revision in Networks with Loops},
institution = {},
year = {1997}
}
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Abstract:
Local belief propagation rules of the sort proposed by Pearl (1988) are guaranteed to converge to the optimal beliefs for singly connected networks. Recently, a number of researchers have empirically demonstrated good performance of these same algorithms on networks with loops, but a theoretical understanding of this performance has yet to be achieved. Here we lay a foundation for an understanding of belief propagation in networks with loops. For networks with a single loop, we derive an analytical relationship between the steady state beliefs in the loopy network and the true posterior probability. Using this relationship we show a category of networks for which the MAP estimate obtained by belief update and by belief revision can be proven to be optimal (although the beliefs will be incorrect). We show how nodes can use local information in the messages they receive in order to correct the steady state beliefs. Furthermore we prove that for all networks with a single loop, the MAP es...
Citations
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| 838 | Near Shannon limit error-correcting coding and decoding – Berrou, Glavieux, et al. - 1993 |
| 293 | Dynamic Programming: Deterministic and Stochastic Models – Bertsekas - 1987 |
| 266 | Good error -correcting codes based on very sparse matrices – MacKay - 1999 |
| 203 | Turbo decoding as an instance of Pearl’s ‘belief propagation’ algorithm – McEliece, MacKay, et al. - 1998 |
| 139 | Probabilistic independence networks for hidden Markov probability models – Smyth, Heckerman, et al. - 1997 |
| 33 | Softoutput decoding algorithms in iterative decoding of turbo-codes – Benedetto, Divsalar, et al. - 1996 |
| 33 | The Turbo decision algorithm – McEliece, Rodemich, et al. - 1995 |
| 15 | Probability propagation and iterative decoding – Frey, Kschischang - 1996 |
