MAP Inference on Million Node Graphical Models: KL-divergence based Alternating Directions Method

Motivated by a problem in large scale climate data analysis, we consider the problem of maximum a posteriori (MAP) inference in graphical models with millions of nodes. While progress has been made in recent years, existing MAP inference algorithms are inherently sequential and hence do not scale well. In this paper, we present a parallel MAP inference algorithm called KL-ADM based on two ideas: tree-decomposition of a graph, and the alternating directions method (ADM). However, unlike standard ADM, we use an inexact ADM augmented with a Kullback-Leibler (KL) divergence based regularization. The unusual modification leads to an efficient iterative algorithm while avoiding double-loops. We rigorously prove global convergence of KL-ADM. We illustrate the effectiveness of KL-ADM through extensive experiments on large synthetic and real datasets. The application on real world precipitation data finds all major droughts in the last century.