Bounding the Partition Function using Holder's Inequality

We describe an algorithm for approximate inference in graphical models based on Hölder’s inequality that provides upper and lower bounds on common summation problems such as computing the partition function or probability of evidence in a graphical model. Our algorithm unifies and extends several existing approaches, including variable elimination techniques such as minibucket elimination and variational methods such as tree reweighted belief propagation and conditional entropy decomposition. We show that our method inherits benefits from each approach to provide significantly better bounds on sum-product tasks.