Related papers: Adapted Optimal Transport between Filtered Gaussia…
A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth…
Optimal transport with quadratic cost provides a geometric framework for steering an ensemble, modeled by a probability law, with minimal effort. Yet ambient-space formulations become unwieldy in high dimensions, and sensing or actuation in…
This article studies the joint problem of uplink-downlink scheduling and power allocation for controlling a large number of actuators that upload their states to remote controllers and download control actions over wireless links. To…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
We obtain an explicit solution for the static Kullback--Leibler (KL) unbalanced optimal transport problem between finite non-degenerate Gaussian measures with quadratic cost, two independent positive marginal relaxation parameters, and no…
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of…
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension. Unlike plug-in rules that simply replace the true distributions by their empirical…
In estimation theory, the Kushner equation provides the evolution of the probability density of the state of a dynamical system given continuous-time observations. Building upon our recent work, we propose a new way to approximate the…
Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that…
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the…
The Gromov-Wasserstein (GW) transport problem is a relaxation of classic optimal transport, which seeks a transport between two measures while preserving their internal geometry. Due to meeting this theoretical underpinning, it is a…
We take a new look at the relation between the optimal transport problem and the Schr\"{o}dinger bridge problem from the stochastic control perspective. We show that the connections are richer and deeper than described in existing…
A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and…
In this work, a flexible higher-order space-time adaptive finite element approximation of convection-dominated transport with coupled fluid flow is developed and studied. Convection-dominated transport is a challenging subproblem in…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
This paper presents a framework for computing the Gromov-Wasserstein problem between two sets of points in low dimensional spaces, where the discrepancy is the squared Euclidean norm. The Gromov-Wasserstein problem is a generalization of…
We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is…
Due to its invariance to rigid transformations such as rotations and reflections, Procrustes-Wasserstein (PW) was introduced in the literature as an optimal transport (OT) distance, alternative to Wasserstein and more suited to tasks such…
Regression analysis for responses taking values in general metric spaces has received increasing attention, particularly for settings with Euclidean predictors $X \in \mathbb{R}^p$ and non-Euclidean responses $Y$ in metric spaces. While…
Flow matching has recently emerged as a flexible and efficient framework for generative modelling by learning deterministic transport dynamics between probability measures. In this work, we extend flow matching to the space of probability…