Proceedings Article10.1109/ITW.2007.4313078
Approximate message-passing inference algorithm
Kyomin Jung,Devavrat Shah +1 more
- 24 Sep 2007
- pp 224-229
TL;DR: A novel tight characterization of the size of self-avoiding walk tree for any connected graph as a function of number of edges and nodes is obtained and can provide provably arbitrarily small error for a large class of graphs including planar graphs.
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Abstract: In a recent result, Weitz (D. Weitz, 2006) established equivalence between the marginal distribution of a node, say G, in any binary pair-wise Markov random field (MRF), say G, with the marginal distribution of the root node in the self-avoid walk tree of the G starting at v. Analogous result for max-marginal distribution holds for the reason that addition and multiplication commute in the same way as addition and maximum. This remarkable connection suggests a message-passing algorithm for computing exact marginal and max-marginal in any binary MRF G. In this paper, we exploit this property along with appropriate graph partitioning scheme to design approximate message passing algorithms for computing max-marginal of nodes or maximum a-posteriori assignment (MAP) in a binary MRF G. Our algorithm can provide provably arbitrarily small error for a large class of graphs including planar graphs. Our algorithms are linear in number of nodes G with constant dependent on the approximation error. For precise evaluation of computation cost of algorithm, we obtain a novel tight characterization of the size of self-avoiding walk tree for any connected graph as a function of number of edges and nodes.
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Judea Pearl
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TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
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Martin J. Wainwright,Michael I. Jordan +1 more
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TL;DR: The variational approach provides a complementary alternative to Markov chain Monte Carlo as a general source of approximation methods for inference in large-scale statistical models.
Convergent Tree-Reweighted Message Passing for Energy Minimization
TL;DR: The sequential tree-reweighted message passing (STE-TRW) algorithm as discussed by the authors is a modification of Tree-Reweighted Maximum Product Message Passing (TRW), which was proposed by Wainwright et al.
MAP estimation via agreement on trees: message-passing and linear programming
TL;DR: This work develops and analyze methods for computing provably optimal maximum a posteriori probability (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles and establishes 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.
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