Geodesic
Optimally approximating exponential families
Kybernetika, Tome 49 (2013) no. 2, pp. 199-215.

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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.
Classification : 62B10, 94A15, 94A17
Keywords: exponential family; information divergence 
@article{KYB_2013__49_2_a0,
     author = {Rauh, Johannes},
     title = {Optimally approximating exponential families},
     journal = {Kybernetika},
     pages = {199--215},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2013},
     mrnumber = {3085392},
     zbl = {06176033},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2013__49_2_a0/}
}
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Rauh, Johannes. Optimally approximating exponential families. Kybernetika, Tome 49 (2013) no. 2, pp. 199-215. http://geodesic.mathdoc.fr/item/KYB_2013__49_2_a0/