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.
Recently REF showed a different connection by using MAP inference on randomly perturbed models to approximate and bound Z.
On the Partition Function and Random Maximum A-Posteriori Perturbations
ICML
Mathematics Computer Science