A correspondence principle for relative entropy minimization

Relative entropy minimization has been proposed as an inference method for problems with information in the form of constraints on the underlying probability model. We provide a theoretical justification for this procedure through a correspondence principle. In particular, for a convex constraints set Λ, we show that as the number of trials increases, the empirical distribution constrained to lie within Λ and associated with a discrete probability distribution p will become arbitrarily close with high probability to the distribution that minimizes the relative entropy between p and Λ.