Maximum persistency via iterative relaxed inference with graphical models

We consider the NP-hard problem of MAP-inference for graphical models. We propose a polynomial time practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks each label in each node of the considered graphical model either as (i) optimal, meaning that it belongs to all optimal solutions of the inference problem; (ii) non-optimal if it provably does not belong to any solution; or (iii) undefined, which means our algorithm can not make a decision regarding the label. Moreover, we prove optimality of our approach: it delivers in a certain sense the largest total number of labels marked as optimal or non-optimal. We demonstrate superiority of our approach on problems from machine learning and computer vision benchmarks.