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Generalized Bregman and Jensen divergences which include some f-divergences

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  • Nishiyama, Tomohiro

Abstract

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 g-Bregman divergence and the skew g-Jensen divergence and show this inequality is a generalization of Lin's inequality.

Suggested Citation

  • Nishiyama, Tomohiro, 2018. "Generalized Bregman and Jensen divergences which include some f-divergences," OSF Preprints ybmdx, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:ybmdx
    DOI: 10.31219/osf.io/ybmdx
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    References listed on IDEAS

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    1. Nishiyama, Tomohiro, 2018. "Divergence Functions in Dually Flat Spaces and Their Properties," OSF Preprints j42n6, Center for Open Science.
    2. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
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    Cited by:

    1. Nishiyama, Tomohiro, 2018. "Divergence Network: Graphical calculation method of divergence functions," OSF Preprints am4pr, Center for Open Science.
    2. Nishiyama, Tomohiro, 2018. "Sum decomposition of divergence into three divergences," OSF Preprints dvcbt, Center for Open Science.

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