A Novel Tree Block-Coordinate Method For Map Inference

Block-coordinate methods inspired by belief propagation are among the most successful methods for approximate MAP inference in graphical models. The set of unknowns optimally updated in such block-coordinate methods is typically very small and spans only single edges or shallow trees. We derive a method that optimally updates sets of unknowns spanned by an arbitrary tree that is different from one reported in the literature. It provides some insight why "tree block-coordinate" methods are not as useful as expected, and enables a simple technique to makes these tree updates more effective.