Focusing generalizations of belief propagation on targeted queries

A recent formalization of Iterative Belief Propagation (IBP) has shown that it can be understood as an exact inference algorithm on an approximate model that results from deleting every model edge. This formalization has led to (1) new realizations of Generalized Belief Propagation (GBP) in which edges are recovered incrementally to improve approximation quality, and (2) edge-recovery heuristics that are motivated by improving the approximation quality of all node marginals in a graphical model. In this paper, we propose new edge-recovery heuristics, which are focused on improving the approximations of targeted node marginals. The new heuristics are based on newly-identified properties of edge deletion, and in turn IBP, which guarantee the exactness of edge deletion in simple and idealized cases. These properties also suggest new improvements to IBP approximations which are based on performing edge-by-edge corrections on targeted marginals, which are less costly than improvements based on edge recovery.