Related papers: A parallel framework for graphical optimal transpo…
Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for…
In this paper, we address the numerical solution to the multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build…
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…
We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…
Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent…
Computationally solving multi-marginal optimal transport (MOT) with squared Euclidean costs for $N$ discrete probability measures has recently attracted considerable attention, in part because of the correspondence of its solutions with…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
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…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…
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…
Complexity of the Operations Research Theory tasks can be often diminished in cases that do not require finding the exact solution. For example, forecasting two-dimensional hierarchical time series leads us to the transportation problem…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…