Beyond Trees: MAP Inference in MRFs via Outer-Planar Decomposition

Maximum a posteriori (MAP) inference in Markov Random Fields (MRFs) is an NP-hard problem, and thus research has focussed on either finding efficiently solvable subclasses (e.g . trees), or approximate algorithms (e.g . Loopy Belief Propagation (BP) and Tree-reweighted (TRW) methods). This paper presents a unifying perspective of these approximate techniques called “Decomposition Methods”. These are methods that decompose the given problem over a graph into tractable subproblems over subgraphs and then employ message passing over these subgraphs to merge the solutions of the subproblems into a global solution. This provides a new way of thinking about BP and TRW as successive steps in a hierarchy of decomposition methods. Using this framework, we take a principled first step towards extending this hierarchy beyond trees. We leverage a new class of graphs amenable to exact inference, called outer-planar graphs, and propose an approximate inference algorithm called Outer-Planar Decomposition (OPD). OPD is a strict generalization of BP and TRW, and contains both of them as special cases. Our experiments show that this extension beyond trees is indeed very powerful – OPD outperforms current state-of-art inferD. Batra ECE Dept., Carnegie Mellon University www.ece.cmu.edu/~dbatra E-mail: [email protected] A. C. Gallagher Electronic Imaging Products, Eastman Kodak Company E-mail: [email protected] D. Parikh Toyota Technological Institute at Chicago E-mail: [email protected] T. Chen ECE Dept., Cornell University ence methods on hard non-submodular synthetic problems and is competitive on real computer vision applications.