Computer Science – Information Theory
Scientific paper
2005-08-15
Computer Science
Information Theory
Presented in part at the Allerton Conference on Communication, Computing and Control in October 2002. Full journal version app
Scientific paper
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex combination of tree-structured distributions, we obtain an upper bound on the optimal value of the original problem (i.e., the log probability of the MAP assignment) in terms of the combined optimal values of the tree problems. We prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common. An important implication is that any such shared configuration must also be a MAP configuration for the original distribution. Next we develop two approaches to attempting to obtain tight upper bounds: (a) a {\em tree-relaxed linear program} (LP), which is derived from the Lagrangian dual of the upper bounds; and (b) a {\em tree-reweighted max-product message-passing algorithm} that is related to but distinct from the max-product algorithm. In this way, we establish a connection between a certain LP relaxation of the mode-finding problem, and a reweighted form of the max-product (min-sum) message-passing algorithm.
Jaakkola Tommi S.
Wainwright Martin J.
Willsky Alan S.
No associations
LandOfFree
MAP estimation via agreement on (hyper)trees: Message-passing and linear programming does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with MAP estimation via agreement on (hyper)trees: Message-passing and linear programming, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and MAP estimation via agreement on (hyper)trees: Message-passing and linear programming will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-138287