The Fourier Discrepancy Function
This work provides a new mathematical tool for comparing discrete probability measures, which could be useful for researchers working on statistical analysis and probability theory.
This paper introduces the Fourier Discrepancy Function, a novel discrepancy measure for comparing discrete probability measures. It is shown to be convex, twice differentiable with an explicit gradient formula, and offers a statistical interpretation, with bounds established in relation to the Total Variation distance.
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.