M. J. Wainwright, T. S. Jaakkola, and A. S. Willsky. Tree consistency and bounds on the performance of the max-product algorithm and its generalizations. Statistics and Computing, 14: 143--166, April 2004.  Home/Search Document Details and Download
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Exact MAP Estimates by (Hyper)tree Agreement - Wainwright, Jaakkola, Willsky Self-citation (Wainwright Jaakkola Willsky) (Correct)
.... ; x t ) max j (x t ) xs ;x t )g With these definitions, the max marginal tree factorization [1] is given by: p(x; T ) T s (x s ) T st (x s ; x t ) T s (x s )T t (x t ) 7) One interpretation of the ordinary max product algorithm for trees, as shown in our previous work [6], is as computing this alternative representation. Suppose moreover that for each node s 2 V , the following uniqueness condition holds: Uniqueness Assumption: The max marginal T s has a unique optimum x s . In this case, the vector x s j s 2 V g is the MAP configuration for the ....
....set of messages M as in equations (9a) and (9b) the convex combination T (T ) log p (x; T) is equivalent to log p(x; b ) up to an additive constant. We now need to ensure that T = fT s ; T st g are a consistent set of max marginals for each tree distribution p (x; T) It is sufficient [1, 6] to impose, for each edge (s; t) the following local consistency condition: max T st (x s ; x t ) T s (x s ) 10) In order to achieve this local consistency, we update the messages in the following manner: Algorithm 1 (Tree reweighted max product) For any e 2 T(G) with e 0 ....
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M. J. Wainwright, T. Jaakkola, and A. S. Willsky. Tree consistency and bounds on the performance of the max-product algorithm and its generalizations. LIDS Tech. report, June 2002.
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M. J. Wainwright, T. Jaakkola, and A. S. Willsky, "Tree consistency and bounds on the performance of the max-product algorithm and its generalizations," Tech. Rep. LIDS P-2554, Laboratory for Information and Decision Systems, MIT, Cambridge, MA, July 2002.
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M. J. Wainwright, T. S. Jaakkola, and A. S. Willsky. Tree consistency and bounds on the performance of the max-product algorithm and its generalizations. Statistics and Computing, 14: 143--166, April 2004.
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M. J. Wainwright, T. Jaakkola, A. S. Willsky, Tree consistency and bounds on the performance of the max-product algorithm and its generalizations, Statistics and Computing 14 (2004) 143--166.
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M. Wainwright, T. Jaakkola, and A. Willsky. Tree consistency and bounds on the performance of the maxproduct algorithm and its generalizations. Technical report, P-2554, LIDS-MIT, 2002.
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M. J. Wainwright, T. Jaakkola, and A. S. Willsky. Tree consistency and bounds on the performance of the max-product algorithm and its generalizations. Technical Report P-2554, MIT LIDS, 2002.
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