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Full--waveform inversion (FWI) is a method used to determine properties of the Earth from information on the surface. We use the squared Wasserstein distance (squared $W_2$ distance) as an objective function to invert for the velocity of…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients…
We investigate here the optimal transportation problem on configuration space for the quadratic cost. It is shown that, as usual, provided that the corresponding Wasserstein is finite, there exists one unique optimal measure and that this…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
This work is concerned with the classical problem of finding a zero of a sum of maximal monotone operators. For the projective splitting framework recently proposed by Combettes and Eckstein, we show how to replace the fundamental…
We study first-order optimality conditions for constrained optimization in the Wasserstein space, whereby one seeks to minimize a real-valued function over the space of probability measures endowed with the Wasserstein distance. Our…
In this work, we present a method to compute the Kantorovich-Wasserstein distance of order one between a pair of two-dimensional histograms. Recent works in Computer Vision and Machine Learning have shown the benefits of measuring…
Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of…
Matching a source to a target probability measure is often solved by instantiating a linear optimal transport (OT) problem, parameterized by a ground cost function that quantifies discrepancy between points. When these measures live in the…
Collaborative learning has recently achieved very significant results. It still suffers, however, from several issues, including the type of information that needs to be exchanged, the criteria for stopping and how to choose the right…
Evolutionary algorithms (EAs) are promising approaches for non-differentiable or strongly multimodal topology optimization problems, but they often suffer from the curse of dimensionality, generally leading to low-resolution optimized…
Anomaly detection is a promising, model-agnostic strategy to find physics beyond the Standard Model. State-of-the-art machine learning methods offer impressive performance on anomaly detection tasks, but interpretability, resource, and…
We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
Computing optimal transport (OT) between measures in high dimensions is doomed by the curse of dimensionality. A popular approach to avoid this curse is to project input measures on lower-dimensional subspaces (1D lines in the case of…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…
This paper focuses on the Monge-Kantorovich formulation of the optimal transport problem and the associated $L^2$ Wasserstein distance. We use the $L^2$ Wasserstein distance in the Nearest Neighbour (NN) machine learning architecture to…