In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As a result, we can use efficient MAP solvers such as graph-cuts to evaluate the corresponding partition function. We show that our method excels in the typical "high signal -high coupling" regime that results in ragged energy landscapes difficult for alternative approaches.
The basis of our work is REF which provides a framework for approximating and bounding the partition function using MAP 1 inference (i.e. prediction of the most likely structure) on randomly perturbed models.
On the Partition Function and Random Maximum A-Posteriori Perturbations
ICML
Mathematics Computer Science