2 citations · 4 across the 17 of their papers we have counts for
6 papers · 1 filter
On Rank Graduation Metrics for High Dimensional Ordinal Data
Gennaro Auricchio, Adelaide Emma Bernardelli, Paolo Giudici +1
Evaluating the reliability of machine learning classifications remains a fundamental challenge in Artificial Intelligence (AI), particularly when the target variable is multidimens…
On the computation of the infinity Wasserstein distance and the Wasserstein Projection Problem
Gennaro Auricchio, Gabriele Loli, Marco Veneroni
Computing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various ap…
On the Pythagorean Structure of the Optimal Transport for Separable Cost Functions
Gennaro Auricchio
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimens…
On the Structure of Optimal Transportation Plans between Discrete Measures
Gennaro Auricchio, Marco Veneroni
In this paper, we prove a structure theorem for discrete optimal transportation plans. We show that, given any pair of discrete probability measures and a cost function, there exis…
The Equivalence of Fourier-based and Wasserstein Metrics on Imaging Problems
Gennaro Auricchio, Andrea Codegoni, Stefano Gualandi +2
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spat…
Computing Kantorovich-Wasserstein Distances on -dimensional histograms using -partite graphs
Gennaro Auricchio, Federico Bassetti, Stefano Gualandi +1
This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of -dimensional histograms having bins each. We prove that this probl…