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Gibbs sampling on factor graphs is a widely used inference technique, whichoften produces good empirical results. Theoretical guarantees for itsperformance are weak: even for tree structured graphs, the mixing time of Gibbsmay be exponential in the number of variables. To help understand the behaviorof Gibbs sampling, we introduce a new (hyper)graph property, called hierarchywidth. We show that under suitable conditions on the weights, bounded hierarchywidth ensures polynomial mixing time. Our study of hierarchy width is in partmotivated by a class of factor graph templates, hierarchical templates, whichhave bounded hierarchy width---regardless of the data used to instantiate them.We demonstrate a rich application from natural language processing in whichGibbs sampling provably mixes rapidly and achieves accuracy that exceeds humanvolunteers.

Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width