Local approximate inference algorithms
Abstract
We present a new local approximation algorithm for computing Maximum a Posteriori (MAP) and logpartition function for arbitrary exponential family distribution represented by a finitevalued pairwise Markov random field (MRF), say $G$. Our algorithm is based on decomposition of $G$ into {\em appropriately} chosen small components; then computing estimates locally in each of these components and then producing a {\em good} global solution. We show that if the underlying graph $G$ either excludes some finitesized graph as its minor (e.g. Planar graph) or has low doubling dimension (e.g. any graph with {\em geometry}), then our algorithm will produce solution for both questions within {\em arbitrary accuracy}. We present a messagepassing implementation of our algorithm for MAP computation using selfavoiding walk of graph. In order to evaluate the computational cost of this implementation, we derive novel tight bounds on the size of selfavoiding walk tree for arbitrary graph. As a consequence of our algorithmic result, we show that the normalized logpartition function (also known as freeenergy) for a class of {\em regular} MRFs will converge to a limit, that is computable to an arbitrary accuracy.
 Publication:

arXiv eprints
 Pub Date:
 October 2006
 DOI:
 10.48550/arXiv.cs/0610111
 arXiv:
 arXiv:cs/0610111
 Bibcode:
 2006cs.......10111J
 Keywords:

 Computer Science  Artificial Intelligence
 EPrint:
 21 pages, 10 figures