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Sum decomposition of divergence into three divergences

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  • Nishiyama, Tomohiro

Abstract

Divergence functions play a key role as to measure the discrepancy between two points in the field of machine learning, statistics and signal processing. Well-known divergences are the Bregman divergences, the Jensen divergences and the f-divergences. In this paper, we show that the symmetric Bregman divergence can be decomposed into the sum of two types of Jensen divergences and the Bregman divergence. Furthermore, applying this result, we show another sum decomposition of divergence is possible which includes f-divergences explicitly.

Suggested Citation

  • Nishiyama, Tomohiro, 2018. "Sum decomposition of divergence into three divergences," OSF Preprints dvcbt, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:dvcbt
    DOI: 10.31219/osf.io/dvcbt
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    1. Nishiyama, Tomohiro, 2018. "Generalized Bregman and Jensen divergences which include some f-divergences," OSF Preprints ybmdx, Center for Open Science.
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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.

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    1. Nishiyama, Tomohiro, 2018. "Divergence Network: Graphical calculation method of divergence functions," OSF Preprints am4pr, Center for Open Science.

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