Subproblem-Tree Calibration: A Unified Approach to Max-Product Message Passing

Max-product (max-sum) message passing algorithms are widely used for MAP inference in MRFs. It has many variants sharing a common flavor of passing "messages" over some graph-object. Recent advances revealed that its convergent versions (such as MPLP, MSD, TRW-S) can be viewed as performing block coordinate descent (BCD) in a dual objective. That is, each BCD step achieves dual-optimal w.r.t. a block of dual variables (messages), thereby decreases the dual objective monotonically. However, most existing algorithms are limited to updating blocks selected in rather restricted ways. In this paper, we show a "unified" message passing algorithm that: (a) subsumes MPLP, MSD, and TRW-S as special cases when applied to their respective choices of dual objective and blocks, and (b) is able to perform BCD under much more flexible choices of blocks (including very large blocks) as well as the dual objective itself (that arise from an arbitrary dual decomposition).