The Fourier Discrepancy Function
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Abstract (arXiv)
In this paper, we propose the Fourier Discrepancy Function, a new discrepancy to compare discrete probability measures. We show that this discrepancy takes into account the geometry of the underlying space. We prove that the Fourier Discrepancy is convex, twice differentiable, and that its gradient has an explicit formula. We also provide a compelling statistical interpretation. Finally, we study the lower and upper tight bounds for the Fourier Discrepancy in terms of the Total Variation distance.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 10 of its 44 references that are in the map. First posted on arXiv 5 Feb 2021.
Builds on
10 of 44 references.
References · 10
- 2014Deep Learning in Neural Networks: An Overviewcited by 765
- 2017Robust Loss Functions under Label Noise for Deep Neural Networkscited by 441
- 2017MMD GAN: Towards Deeper Understanding of Moment Matching Networkcited by 251
- 2013Fast Computation of Wasserstein Barycenterscited by 216
- 2015Learning with a Wasserstein Losscited by 194
- 2017On Loss Functions for Deep Neural Networks in Classificationcited by 68
- 2019A Characteristic Function Approach to Deep Implicit Generative Modelingcited by 25
- 2018Computing Kantorovich-Wasserstein Distances on d-dimensional histograms using (d+1)-partite graphscited by 4
- 2013Sharp Inequalities for f-divergencescited by 3
- 2020The Equivalence of Fourier-based and Wasserstein Metrics on Imaging Problemscited by 3
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Citing papers per year: 2025: 1.
1 paper.