Related papers: A Vectorial Approach to Unbalanced Optimal Mass Tr…
Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitioners have access to samples which approximate the continuous…
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…
While optimal transport (OT) enforces a rigid constraint by requiring two measures to be matched exactly, partial optimal transport relaxes this requirement by allowing mass to remain unmatched through a global budget, scalar rebate, or…
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) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
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…
Branched Optimal Transport (BOT) is a generalization of optimal transport in which transportation costs along an edge are subadditive. This subadditivity models an increase in transport efficiency when shipping mass along the same route,…
Unbalanced optimal transport (UOT) provides a flexible way to match or compare nonnegative finite Radon measures. However, UOT requires a predefined ground transport cost, which may misrepresent the data's underlying geometry. Choosing such…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
An optimal transport (OT) problem seeks to find the cheapest mapping between two distributions with equal total density, given the cost of transporting density from one place to another. Unbalanced OT allows for different total density in…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…
We provide a computational complexity analysis for the Sinkhorn algorithm that solves the entropic regularized Unbalanced Optimal Transport (UOT) problem between two measures of possibly different masses with at most $n$ components. We show…
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…
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 study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…
Optimal transport has found widespread applications in signal processing and machine learning. Among its many equivalent formulations, optimal transport seeks to reconstruct a random variable/vector with a prescribed distribution at the…
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…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
As a powerful technique in generative modeling, Flow Matching (FM) aims to learn velocity fields from noise to data, which is often explained and implemented as solving Optimal Transport (OT) problems. In this study, we bridge FM and the…