Codivergences and information matrices

03/14/2023

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by   Alexis Derumigny, et al.

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We propose a new concept of codivergence, which quantifies the similarity between two probability measures P_1, P_2 relative to a reference probability measure P_0. In the neighborhood of the reference measure P_0, a codivergence behaves like an inner product between the measures P_1 - P_0 and P_2 - P_0. Two specific codivergences, the χ^2-codivergence and the Hellinger codivergence are introduced and studied. We derive explicit expressions for several common parametric families of probability distributions. For a codivergence, we introduce moreover the divergence matrix as an analogue of the Gram matrix. It is shown that the χ^2-divergence matrix satisfies a data-processing inequality.