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arXiv · 2003.02469

Cumulant-free closed-form formulas for some common (dis)similarities between densities of an exponential family

Frank Nielsen·Richard Nock
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Abstract

It is well-known that the Bhattacharyya, Hellinger, Kullback-Leibler, $\alpha$-divergences, and Jeffreys' divergences between densities belonging to a same exponential family have generic closed-form formulas relying on the strictly convex and real-analytic cumulant function characterizing the exponential family. In this work, we report (dis)similarity formulas which bypass the explicit use of the cumulant function and highlight the role of quasi-arithmetic means and their multivariate mean operator extensions. In practice, these cumulant-free formulas are handy when implementing these (dis)similarities using legacy Application Programming Interfaces (APIs) since our method requires only to partially factorize the densities canonically of the considered exponential family.

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Frank Nielsen, Richard Nock. 2020-03-05. Cumulant-free closed-form formulas for some common (dis)similarities between densities of an exponential family. https://arxiv.org/abs/2003.02469

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