Séminaire LFI
Choquet-Wasserstein pseudo-distances via optimal transport in Dempster-Shafer theory
18/04/2024Intervenant(s) : Davide PETTURITI (Dpt of Economics, University of Perugia, Italy)
Résumé: The marginal problem is considered in Dempster-Shafer theory, by investigating the structure of a suitable set of bivariate joint belief functions having fixed marginals, through copula theory. Next, we formulate two Kantorovich-like optimal transport problems, either seeking to minimize the Choquet integral of a given cost function with respect to the reference set of joint belief functions or its dual functional. A noticeable application is obtained by choosing a metric as cost function: this permits to define pessimistic and optimistic Choquet-Wasserstein pseudo-distances, that can be used to compare belief functions on the same space. Finally, given an arbitrary belief function, we address the problem of computing a “closest” belief function in some distinguished sub-classes, by minimizing one of the two Choquet-Wasserstein pseudo-distances. [Work in collaboration with Silvia Lorenzini (University of Perugia) and Barbara Vantaggi (Sapienza University of Roma)]
Bio : Davide Petturiti is Associate Professor in Mathematical Methods for Economics and Actuarial and Financial Sciences, in the Department of Economics, at the University of Perugia (Italy) since 2019. He obtained his qualifications to the functions of Professor in Italy (ASN) in Mathematical Analysis, Probability and Statistics in 2021, and in Mathematical Methods for Economics and Actuarial and Financial Sciences in 2020. His research work focuses on artificial intelligence and decision theory.
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