Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Gamma-Divergence. An Introduction to New Divergence Family

Version 1 : Received: 11 November 2020 / Approved: 13 November 2020 / Online: 13 November 2020 (15:45:32 CET)

How to cite: Riveaud, L.; Diego, M.; Lamberti, P.W. Gamma-Divergence. An Introduction to New Divergence Family. Preprints 2020, 2020110388 (doi: 10.20944/preprints202011.0388.v1). Riveaud, L.; Diego, M.; Lamberti, P.W. Gamma-Divergence. An Introduction to New Divergence Family. Preprints 2020, 2020110388 (doi: 10.20944/preprints202011.0388.v1).

Abstract

Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application, a more appropriate measure may be necessary. In this paper we introduce a family of divergences called γ-Divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. In addition, we define a generalised entropy closely related to the γ-Divergences. Finally, we apply our findings to the analysis of simulated and real time series.

Subject Areas

Information Theory; Entropy; Divergence; Divergence families

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