A family of statistical symmetric divergences based on Jensen's inequality

Frank Nielsen

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arXiv · 1009.4004

A family of statistical symmetric divergences based on Jensen's inequality

Frank Nielsen

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Abstract

We introduce a novel parametric family of symmetric information-theoretic distances based on Jensen's inequality for a convex functional generator. In particular, this family unifies the celebrated Jeffreys divergence with the Jensen-Shannon divergence when the Shannon entropy generator is chosen. We then design a generic algorithm to compute the unique centroid defined as the minimum average divergence. This yields a smooth family of centroids linking the Jeffreys to the Jensen-Shannon centroid. Finally, we report on our experimental results.

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Frank Nielsen. 2011-12-19. A family of statistical symmetric divergences based on Jensen's inequality. https://arxiv.org/abs/1009.4004

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