MAP Estimation for Graphical Models by Likelihood Maximization

Computing a maximum a posteriori (MAP) assignment in graphical models is a crucial inference problem for many practical applications. Several provably convergent approaches have been successfully developed using linear programming (LP) relaxation of the MAP problem. We present an alternative approach, which transforms the MAP problem into that of inference in a mixture of simple Bayes nets. We then derive the Expectation Maximization (EM) algorithm for this mixture that also monotonically increases a lower bound on the MAP assignment until convergence. The update equations for the EM algorithm are remarkably simple, both conceptually and computationally, and can be implemented using a graph-based message passing paradigm similar to max-product computation. Experiments on the real-world protein design dataset show that EM’s convergence rate is significantly higher than the previous LP relaxation based approach MPLP. EM also achieves a solution quality within 95% of optimal for most instances.