Generalized Bregman and Jensen divergences which include some f-divergences

08/19/2018

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by   Tomohiro Nishiyama, et al.

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In this paper, we introduce new classes of divergences by extending the definitions of the Bregman divergence and the skew Jensen divergence. These new divergence classes (g-Bregman divergence and skew g-Jensen divergence) satisfy some properties similar to the Bregman or skew Jensen divergence. We show these g-divergences include divergences which belong to a class of f-divergence (the Hellinger distance, the chi-square divergence and the alpha-divergence in addition to the Kullback-Leibler divergence). Moreover, we derive an inequality between the skew g-Jensen divergence and the g-Bregman divergence and show this inequality is a generalization of Lin's inequality.