We introduce a novel method for estimating the partition function and marginals of distributions defined using graphical models. The method uses the entropy chain rule to obtain an upper bound on the entropy of a distribution given marginal distributions of variable subsets. The structure of the bound is determined by a permutation, or elimination order, of the model variables. Optimizing this bound results in an upper bound on the log partition function, and also yields an approximation to the model marginals. The optimization problem is convex, and is in fact a dual of a geometric program. We evaluate the method on a 2D Ising model with a wide range of parameters, and show that it compares favorably with previous methods in terms of both partition function bound, and accuracy of marginals.
|Number of pages||9|
|Journal||Journal of Machine Learning Research|
|State||Published - 2007|
|Event||11th International Conference on Artificial Intelligence and Statistics, AISTATS 2007 - San Juan, Puerto Rico|
Duration: 21 Mar 2007 → 24 Mar 2007