Optimally approximating exponential families

Johannes Rauh

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arXiv · 1111.0483

Optimally approximating exponential families

Johannes Rauh

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Abstract

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.

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Johannes Rauh. 2011-11-02. Optimally approximating exponential families. https://arxiv.org/abs/1111.0483

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