Finding the Maximizers of the Information Divergence from an Exponential Family

Details Finding the Maximizers of the Information Divergence from an Exponential Family Finding the Maximizers of the Information Divergence from an Exponential Family

2009-12-23

arxiv.org/abs/0912.4660v1

Computer Science

Information Theory

25 pages

Scientific paper

This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint support and the same value of the sufficient statistics $A$. This observation can be used to transform the original problem of maximizing $D(\cdot||E)$ over the set of all probability measures into the maximization of a function $\Dbar$ over a convex subset of $\ker A$. The global maximizers of both problems correspond to each other. Furthermore, finding all local maximizers of $\Dbar$ yields all local maximizers of $D(\cdot||E)$. This paper also proposes two algorithms to find the maximizers of $\Dbar$ and applies them to two examples, where the maximizers of $D(\cdot||E)$ were not known before.

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