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MiS Preprint

On maximization of the information divergence from an exponential family

František Matúš and Nihat Ay


The information divergence of a probability measure $P$ from an exponential family $\mathcal{E}$ over a finite set is defined as infimum of the divergences of $P$ from $Q$ subject to $Q$ in $\mathcal{E}$. For convex exponential families the local maximizers of this function of $P$ are found. General exponential family $\mathcal{E}$ of dimension $d$ is enlarged to an exponential family $\mathcal{E}^*$ of the dimension at most $3d+2$ such that the local maximizers are of zero divergence from $\mathcal{E}^*$.

MSC Codes:
94A17, 62B10, 60A10
kullback-leibler divergence, information projection, exponential family, infomax principle

Related publications

2003 Repository Open Access
František Matúš and Nihat Ay

On maximization of the information divergence from an exponential family

In: Proceedings of 6th workshop on uncertainty processing : Hejnice, September 24-27, 2003
[Praha] : Oeconomica, 2003. - pp. 199-204