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 applied fields. However, the practical applicability of these objects is limited by two factors: either the associated quantities are computationally prohibitive or there is a lack of available algorithms capable of calculating them. In this paper, we propose a novel class of Linear Programming problems and a routine that allows us to compute the infinity Wasserstein distance and to compute a projection of a probability measure over a generic subset of probability measures with respect to any 𝑝-Wasserstein distance with 𝑝 ∈ [1, ∞].
On the computation of the infinity Wasserstein distance and the Wasserstein Projection Problem
Auricchio, Gennaro;Loli, Gabriele;Veneroni, Marco
2025-01-01
Abstract
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 applied fields. However, the practical applicability of these objects is limited by two factors: either the associated quantities are computationally prohibitive or there is a lack of available algorithms capable of calculating them. In this paper, we propose a novel class of Linear Programming problems and a routine that allows us to compute the infinity Wasserstein distance and to compute a projection of a probability measure over a generic subset of probability measures with respect to any 𝑝-Wasserstein distance with 𝑝 ∈ [1, ∞].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
