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MiS Preprint

Optimally approximating exponential families

Johannes Rauh


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. 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.

Oct 28, 2011
Nov 2, 2011
MSC Codes:
62E17, 94A17, 60E05
exponential family, information divergence, hierarchical models

Related publications

2013 Journal Open Access
Johannes Rauh

Optimally approximating exponential families

In: Kybernetika, 49 (2013) 2, pp. 199-215