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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.

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  • Nishiyama, Tomohiro, 2018. "Sum decomposition of divergence into three divergences," OSF Preprints dvcbt_v1, Center for Open Science.
    • Handle: RePEc:osf:osfxxx:dvcbt_v1
    DOI: 10.31219/osf.io/dvcbt_v1
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