Related papers: An Efficient Orlicz-Sobolev Approach for Transport…
Regularized optimal transport (OT) is now increasingly used as a loss or as a matching layer in neural networks. Entropy-regularized OT can be computed using the Sinkhorn algorithm but it leads to fully-dense transportation plans, meaning…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…
This paper proposes the use of the Hellinger--Kantorovich metric from unbalanced optimal transport (UOT) in a dimensionality reduction and learning (supervised and unsupervised) pipeline. The performance of UOT is compared to that of…
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…
Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative…
Unsupervised graph alignment aims to find the node correspondence across different graphs without any anchor node pairs. Despite the recent efforts utilizing deep learning-based techniques, such as the embedding and optimal transport…
Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…
Semi-discrete optimal transport (SOT), which maps a continuous probability measure to a discrete one, is a fundamental problem with wide-ranging applications. Entropic regularization is often employed to solve the SOT problem, leading to a…
The theory of weak optimal transport (WOT), introduced by [Gozlan et al., 2017], generalizes the classic Monge-Kantorovich framework by allowing the transport cost between one point and the points it is matched with to be nonlinear. In the…
Comparing time series in a principled manner requires capturing both temporal alignment and distributional similarity of features. Optimal transport (OT) has recently emerged as a powerful tool for this task, but existing OT-based…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
Optimal transport (OT) and unbalanced optimal transport (UOT) are central in many machine learning, statistics and engineering applications. 1D OT is easily solved, with complexity O(n log n), but no efficient algorithm was known for 1D…
Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
This article introduces a new notion of optimal transport (OT) between tensor fields, which are measures whose values are positive semidefinite (PSD) matrices. This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the…