In this paper, we introduce the p-Fourier Discrepancy Functions, a new family of metrics for comparing discrete probability measures, inspired by the χr-metrics. Unlike the χr-metrics, the p-Fourier Discrepancies are well-defined for any pair of measures. We prove that the p-Fourier Discrepancies are convex, twice differentiable, and that their gradient has an explicit formula. Moreover, we study the lower and upper tight bounds for the p-Fourier Discrepancies in terms of the Total Variation distance.
The Fourier Discrepancy Function
Auricchio, GennaroMembro del Collaboration Group
;Codegoni, AndreaMembro del Collaboration Group
;Gualandi, Stefano
Membro del Collaboration Group
;Zambon, LorenzoMembro del Collaboration Group
2023-01-01
Abstract
In this paper, we introduce the p-Fourier Discrepancy Functions, a new family of metrics for comparing discrete probability measures, inspired by the χr-metrics. Unlike the χr-metrics, the p-Fourier Discrepancies are well-defined for any pair of measures. We prove that the p-Fourier Discrepancies are convex, twice differentiable, and that their gradient has an explicit formula. Moreover, we study the lower and upper tight bounds for the p-Fourier Discrepancies in terms of the Total Variation distance.File in questo prodotto:
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