4 citations · 5 across the 7 of their papers we have counts for
8 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 recently…
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…
Extending the Gini Index to Higher Dimensions via Whitening Processes
Gennaro Auricchio, Paolo Giudici, Giuseppe Toscani
Measuring the degree of inequality expressed by a multivariate statistical distribution is a challenging problem, which appears in many fields of science and engineering. In this p…
Measuring multidimensional inequality: a new proposal based on the Fourier transform
Paolo Giudici, Emanuela Raffinetti, Giuseppe Toscani
Inequality measures are quantitative measures that take values in the unit interval, with a zero value characterizing perfect equality. Although originally proposed to measure econ…
Measuring multidimensional heterogeneity in emergent social phenomena
Giuseppe Toscani
Measuring inequalities in a multidimensional framework is a challenging problem which is common to most field of science and engineering. Nevertheless, despite the enormous amount…