A generalization of the α-divergences based on comparable and distinct weighted means

01/27/2020

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by   Frank Nielsen, et al.

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We generalize the renown family of α-divergences in information geometry using comparable and distinct weighted means. After general definitions, we report the explicit closed-form formula for the quasi-arithmetic α-divergences and its subfamily of power α-divergences, including their limit cases of α=0 and α=1, generalizations of the Kullback-Leibler divergence and the reverse Kullback-Leibler divergence, respectively.