Markov Chain Sampling in Discrete Probabilistic Models with Constraints

We study probability measures induced by set functions with constraints. Such measures arise in a variety of real-world settings, where often limited resources, prior knowledge, or other pragmatic considerations can impose hard constraints (e.g., cardinality constraints). For a variety of such probabilistic models, we present theoretical results on mixing times of Markov chains, and show sufficient conditions under which the associated chains mix rapidly. We illustrate our claims by empirically verifying the dependence of mixing times on the key factors that govern our theoretical bounds.