5 papers
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…
Energy distance and evolution problems: a promising tool for kinetic equations
Gennaro Auricchio, Giuseppe Toscani
We study the rate of convergence to equilibrium of the solutions to Fokker-Planck type equations with linear drift by means of Cramér and Energy distances, which have been recentl…
From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
Gennaro Auricchio, Giovanni Brigati, Paolo Giudici +1
Selecting an appropriate divergence measure is a critical aspect of machine learning, as it directly impacts model performance. Among the most widely used, we find the Kullback-Lei…
How to measure multidimensional variation?
Gennaro Auricchio, Paolo Giudici, Giuseppe Toscani
The coefficient of variation, which measures the variability of a distribution from its mean, is not uniquely defined in the multidimensional case, and so is the multidimensional G…
Multivariate Gini-type discrepancies
Gennaro Auricchio, Giovanni Brigati, Paolo Giudici +1
Measuring distances in a multidimensional setting is a challenging problem, which appears in many fields of science and engineering. In this paper, to measure the distance between…