Results 61 to 70 of about 24,182 (212)

Bounding adapted Wasserstein metrics

The Wasserstein distance $\mathcal{W}_p$ is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well studied in recent years.
Blanchet, Jose, Larsson, Martin, Park, Jonghwa, Wiesel, Johannes   +3 more
openaire   +2 more sources

Distributionally robust joint chance-constrained programming with Wasserstein metric

Optimization Methods and Software, 2023
In this paper, we develop an exact reformulation and a deterministic approximation for distributionally robust joint chance-constrained programmings (DRCCPs) with a general class of convex uncertain constraints under data-driven Wasserstein ambiguity sets.
Gu, Yining, Wang, Yanjun
openaire   +2 more sources

Covariance Structure Modeling of Engineering Demand Parameters in Cloud‐Based Seismic Analysis

Earthquake Engineering &Structural Dynamics, EarlyView.
ABSTRACT Probabilistic seismic demand modeling aims to estimate structural demand as a function of ground motion intensity—a critical stage in seismic risk assessment. Although many models exist to describe the structural demand, few consider the covariance among engineering demand parameters, potentially overlooking a key factor in improving the ...
Archie Rudman, Enrico Tubaldi, Roberto Gentile, John Douglas   +3 more
wiley   +1 more source

Exploring the Limitations of Federated Learning: A Novel Wasserstein Metric-Based Poisoning Attack on Traffic Sign Classification

IEEE Access
Federated Learning (FL) enhances privacy but remains vulnerable to model poisoning attacks, where an adversary manipulates client models to upload poisoned updates during training, thereby compromising the overall FL model.
Suzan Almutairi, Ahmed Barnawi
doaj   +1 more source

A Lack of Ricci Bounds for the Entropic Measure on Wasserstein space over the Interval

, 2012
This is a condensed form of the author's essay, which can be found at [arXiv:1105.2883]. We prove that the entropic measure constructed by von Renesse-Sturm over Wasserstein space on the unit interval (probability measures on the unit interval equipped ...
Chodosh, Cordero-Erausquin, Döring, Fukushima, Gigli, Lebedev, Lott, Lott, McCann, Otis Chodosh, Otto, Otto, Sturm, Sturm, Sturm, Villani, Villani, von Renesse, von Renesse   +18 more
core   +1 more source

Metric Currents and Geometry of Wasserstein Spaces

Rendiconti del Seminario Matematico della Università di Padova, 2010
We investigate some geometric aspects of Wasserstein spaces through the continuity equation as worked out in mass transportation theory. By defining a suitable homology on the flat torus \mathbb T^n , we prove that the space
openaire   +2 more sources

Permutation invariant networks to learn Wasserstein metrics

, 2020
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine learning community especially for its principled way of comparing distributions.
Sehanobish, Arijit, Ravindra, Neal, van Dijk, David   +2 more
openaire   +2 more sources

Extending the Wasserstein metric to positive measures

, 2023
We define a metric in the space of positive finite positive measures that extends the 2-Wasserstein metric, i.e. its restriction to the set of probability measures is the 2-Wasserstein metric. We prove a dual and a dynamic formulation and extend the gradient flow machinery of the Wasserstein space. In addition, we relate the barycenter in this space to
Leblanc, Hugo, Gouic, Thibaut Le, Liandrat, Jacques, Tournus, Magali   +3 more
openaire   +2 more sources

Esterification enhances carotenoid retention during bread‐making

Journal of the Science of Food and Agriculture, EarlyView.
Abstract BACKGROUND Carotenoids are plant‐derived antioxidants that contribute to human health and represent key quality traits in wheat‐based foods. However, they are highly unstable and prone to degradation during processing. Xanthophyll esterification has been identified as a natural mechanism that enhances carotenoid stability during grain storage.
María D Requena‐Ramírez, Cristina Rodríguez‐Suárez, Dámaso Hornero‐Méndez, Sergio G Atienza   +3 more
wiley   +1 more source

A View on Optimal Transport from Noncommutative Geometry

Symmetry, Integrability and Geometry: Methods and Applications, 2010
We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry.
Francesco D'Andrea, Pierre Martinetti
doaj   +1 more source