Gamma-Divergence

Leonardo Riveaud; Mateos Diego; Pedro Walter Lamberti

Working Paper Article Version 3 This version is not peer-reviewed

Version 1 : Received: 11 November 2020 / Approved: 13 November 2020 / Online: 13 November 2020 (15:45:32 CET)
Version 2 : Received: 27 May 2021 / Approved: 28 May 2021 / Online: 28 May 2021 (11:53:11 CEST)
Version 3 : Received: 28 June 2021 / Approved: 29 June 2021 / Online: 29 June 2021 (11:37:12 CEST)
Version 4 : Received: 2 September 2021 / Approved: 3 September 2021 / Online: 3 September 2021 (10:26:53 CEST)

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 we call gamma-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. We investigate their properties in the context of kernel theory. Finally, we apply our findings to the analysis of simulated and real time series.

Divergences; Kernels; Time series analysis

Physical Sciences, Acoustics

Comment 1

Received: 29 June 2021
Commenter: Mateos Diego
Commenter's Conflict of Interests: Author

Comment: We add more information on the relationship and use of divergences in the physical sciences

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Gamma-Divergence

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