Approximating the Log-Partition Function

Abstract

Graphical Models are used to represent structural information on a high-dimensional joint probability distribution. Their expressiveness offers simple reductions from a large number of NP-hard problems to inference tasks such as computing the partition function (exact inference) or approximating the log-partition function (approximate inference). In this master thesis, we will motivate the need for a general constant-factor approximations of the log-partition function and prove that a variant of the well studied tree-reweighted algorithm [1] achieves constant factor guarantees. We will express the corresponding approximation ratio 𝜅(𝐺) solely as a function of the graph structure 𝐺.