Distributed Anytime MAP Inference
This addresses the scalability challenge for MAP inference in large graphical models, though it appears incremental as an adaptation of existing decomposition principles to this domain.
The authors tackled the problem of performing MAP inference in graphical models that are too large to fit in memory by developing a distributed anytime algorithm based on a linear programming relaxation and Dantzig-Wolfe decomposition. Experimental results show the algorithm outperforms most current methods in solution quality and scales well to large problems.
We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that allows application of the Dantzig-Wolfe decomposition principle. Subprograms are defined over individual edges and can be computed in a distributed manner. This accommodates solutions to graphs whose state space does not fit in memory. The decomposition master program is guaranteed to compute the optimal solution in a finite number of iterations, while the solution converges monotonically with each iteration. Formulating the MAP inference problem as a linear program allows additional (global) constraints to be defined; something not possible with message passing algorithms. Experimental results show that our algorithm's solution quality outperforms most current algorithms and it scales well to large problems.