Minimax Entropy Principle and Its Application to Texture Modeling

Abstract

Summary:This article studies exponential families $\mathcal{E}$ on finite sets such that the information divergence $D(P\|\mathcal{E})$ of an arbitrary probability distribution from $\mathcal{E}$ is bounded by some constant $D>0$. A particular class of low-dimensional exponential families that have low values of $D$ can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponential families. The case where $D=\log(2)$ is studied in detail. This case is special, because if $D<\log(2)$, then $\mathcal{E}$ contains all probability measures with full support