Chernoff information of exponential families

Details Chernoff information of exponential families Chernoff information of exponential families

2011-02-14

arxiv.org/abs/1102.2684v1

Computer Science

Information Theory

Scientific paper

Chernoff information upper bounds the probability of error of the optimal Bayesian decision rule for $2$-class classification problems. However, it turns out that in practice the Chernoff bound is hard to calculate or even approximate. In statistics, many usual distributions, such as Gaussians, Poissons or frequency histograms called multinomials, can be handled in the unified framework of exponential families. In this note, we prove that the Chernoff information for members of the same exponential family can be either derived analytically in closed form, or efficiently approximated using a simple geodesic bisection optimization technique based on an exact geometric characterization of the "Chernoff point" on the underlying statistical manifold.

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