Emergent Mind
Generalizing Jensen and Bregman divergences with comparative convexity and the statistical Bhattacharyya distances with comparable means
(1702.04877)
Published Feb 16, 2017
in
cs.IT
,
cs.LG
,
and
math.IT
Abstract
Comparative convexity is a generalization of convexity relying on abstract notions of means. We define the Jensen divergence and the Jensen diversity from the viewpoint of comparative convexity, and show how to obtain the generalized Bregman divergences as limit cases of skewed Jensen divergences. In particular, we report explicit formula of these generalized Bregman divergences when considering quasi-arithmetic means. Finally, we introduce a generalization of the Bhattacharyya statistical distances based on comparative means using relative convexity.
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