Related papers: Scalable Simulation-free Entropic Unbalanced Optim…
Optimal transport as a loss for machine learning optimization problems has recently gained a lot of attention. Building upon recent advances in computational optimal transport, we develop an optimal transport non-negative matrix…
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently…
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…
The theory of Optimal Transport (OT) and Martingale Optimal Transport (MOT) were inspired by problems in economics and finance and have flourished over the past decades, making significant advances in theory and practice. MOT considers the…
Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…
Optimal transport (OT) is a framework that can be used to guide the optimal allocation of a limited amount of resources. The classical OT paradigm does not consider malicious attacks in its formulation and thus the designed transport plan…
Flow matching has recently emerged as a powerful framework for continuous-time generative modeling. However, when applied to long-tailed distributions, standard flow matching suffers from majority bias, producing minority modes with low…
Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…
The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…
We develop a mathematical theory of entropic regularisation of unbalanced optimal transport problems. Focusing on static formulation and relying on the formalism developed for the unregularised case, we show that unbalanced optimal…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $\mu$ and $\nu$. Our work is motivated by the specific setting of Monge-Kantorovich quantiles where…
We establish quantitative global stability estimates, formulated in terms of optimal transport (OT) cost, for inverse point-source problems governed by elliptic and parabolic equations with spatially varying coefficients. The key idea is…
Optimal transport (OT) is a framework that can guide the design of efficient resource allocation strategies in a network of multiple sources and targets. This paper applies discrete OT to a swarm of UAVs in a novel way to achieve…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
In recent years, the machine learning community has increasingly embraced the optimal transport (OT) framework for modeling distributional relationships. In this work, we introduce a sample-based neural solver for computing the Wasserstein…
We propose a numerical algorithm for the computation of multi-marginal optimal transport (MMOT) problems involving general probability measures that are not necessarily discrete. By developing a relaxation scheme in which marginal…
We consider the finite horizon optimal steering of the joint state probability distribution subject to the angular velocity dynamics governed by the Euler equation. The problem and its solution amounts to controlling the spin of a rigid…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of…