Partial Optimality by Pruning for MAP-Inference with General Graphical Models
This provides a more efficient way to find partial optimal solutions for energy minimization in graphical models, which is incremental as it builds on convex relaxation methods.
The paper tackles the NP-hard MAP-inference problem for general graphical models by proposing a polynomial-time algorithm that prunes variables from a convex relaxation solution to obtain a partial optimal integral solution, empirically outperforming previous methods in the number of persistently labeled variables.
We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its optimal non-relaxed integral solution. Our algorithm is initialized with variables taking integral values in the solution of a convex relaxation of the MAP-inference problem and iteratively prunes those, which do not satisfy our criterion for partial optimality. We show that our pruning strategy is in a certain sense theoretically optimal. Also empirically our method outperforms previous approaches in terms of the number of persistently labelled variables. The method is very general, as it is applicable to models with arbitrary factors of an arbitrary order and can employ any solver for the considered relaxed problem. Our method's runtime is determined by the runtime of the convex relaxation solver for the MAP-inference problem.