Fixing Max-Product: Convergent Message Passing Algorithms for MAP LP-Relaxations

We present a novel message passing algorithm for approximating the MAP problem in graphical models. The algorithm is similar in structure to max-product but unlike max-product it always converges, and can be proven to find the exact MAP solution in various settings. The algorithm is derived via block coordinate descent in a dual of the LP relaxation of MAP, but does not require any tunable parameters such as step size or tree weights. We also describe a generalization of the method to cluster based potentials. The new method is tested on synthetic and real-world problems, and compares favorably with previous approaches. Graphical models are an effective approach for modeling complex objects via local interactions. In such models, a distribution over a set of variables is assumed to factor according to cliques of a graph with potentials assigned to each clique. Finding the assignment with highest probability in these models is key to using them in practice, and is often referred to as...

• Type: Conference
• Year: 2007
• Where: NIPS
• Authors: Amir Globerson, Tommi Jaakkola
• Keywords: Graphical Models, Information Technology, Lp Relaxations, MAP Problem, NIPS 2007