相关论文: Fast Algorithms for Computational Optimal Transpor…

We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…

Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…

We introduce Primal-Dual Wasserstein GAN, a new learning algorithm for building latent variable models of the data distribution based on the primal and the dual formulations of the optimal transport (OT) problem. We utilize the primal…

We present a computationally efficient framework, called $\texttt{FlowDRO}$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets while aiming to find continuous worst-case…

Optimal transport (OT) distances are finding evermore applications in machine learning and computer vision, but their wide spread use in larger-scale problems is impeded by their high computational cost. In this work we develop a family of…

The time-fractional optimal transport (OT) and mean-field planning (MFP) models are developed to describe the anomalous transport of the agents in a heterogeneous environment such that their densities are transported from the initial…

Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has…

We propose a new \cu{class-optimal} algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of…

Discrete Wasserstein barycenters correspond to optimal solutions of transportation problems for a set of probability measures with finite support. Discrete barycenters are measures with finite support themselves and exhibit two favorable…

This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…

Origin-Destination Matrix (ODM) estimation is a classical problem in transport engineering aiming to recover flows from every Origin to every Destination from measured traffic counts and a priori model information. In addition to traffic…

System-level decision making in transportation needs to understand day-to-day variation of network flows, which calls for accurate modeling and estimation of probabilistic dynamic travel demand on networks. Most existing studies estimate…

We consider the block coordinate descent methods of Gauss-Seidel type with proximal regularization (BCD-PR), which is a classical method of minimizing general nonconvex objectives under constraints that has a wide range of practical…

This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…

Diffusion Models (DMs) have achieved remarkable progress in generative modeling. However, the mismatch between the forward terminal distribution and reverse initial distribution introduces prior error, leading to deviations of sampling…

A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…

An efficient method for computing solutions to the Optimal Transportation (OT) problem with a wide class of cost functions is presented. The standard linear programming (LP) discretization of the continuous problem becomes intractible for…

The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…

We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only…

We study the complexity of approximating Wassertein barycenter of $m$ discrete measures, or histograms of size $n$ by contrasting two alternative approaches, both using entropic regularization. The first approach is based on the Iterative…