Approximate message-passing inference algorithm

Kyomin Jung, Devavrat Shah
2007 2007 IEEE Information Theory Workshop  
In a recent result, Weitz [13] established equivalence between the marginal distribution of a node, say v, 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
more » ... arginal and max-marginal in any binary MRF. 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. 1-4244-1564-0/07/$25.00
doi:10.1109/itw.2007.4313078 fatcat:dlcmgel3lzf6latyfw2zbeqb5e