| Title: |
The Fourier discrepancy function |
| Authors: |
Gennaro Auricchio; Andrea Codegoni; Stefano Gualandi; Lorenzo Zambon |
| Contributors: |
Auricchio, Gennaro; Codegoni, Andrea; Gualandi, Stefano; Zambon, Lorenzo |
| Publisher Information: |
International Press, Inc. |
| Publication Year: |
2023 |
| Collection: |
Padua Research Archive (IRIS - Università degli Studi di Padova) |
| Description: |
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 |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| Relation: |
info:eu-repo/semantics/altIdentifier/wos/WOS:000945178200002; volume:21; issue:3; firstpage:627; lastpage:639; numberofpages:13; journal:COMMUNICATIONS IN MATHEMATICAL SCIENCES; https://hdl.handle.net/11577/3528343 |
| DOI: |
10.4310/CMS.2023.v21.n3.a2 |
| Availability: |
https://hdl.handle.net/11577/3528343; https://doi.org/10.4310/CMS.2023.v21.n3.a2 |
| Rights: |
info:eu-repo/semantics/openAccess ; license:Accesso libero ; license uri:iris.PUB01 |
| Accession Number: |
edsbas.13897964 |
| Database: |
BASE |