Optimally approximating exponential families

Abstract

This article studies exponential families $\mathcal{E}$ on finite sets such that the information divergence $D(P\Vert \mathcal{E})$ 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. Exponential families where $D=\log (2)$ are studied in detail. This case is special, because if $D<\log (2)$, then $\mathcal{E}$ contains all probability measures with full support.

17 pages

References in corpus (1)

• On the toric algebra of graphical models