相关论文: Sliced Optimal Partial Transport

Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…

Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate 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 propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…

Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in…

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 optimal transport (OT) problem for probability measures supported on a tree metric space. It is known that such OT problem (i.e., tree-Wasserstein (TW)) admits a closed-form expression, but depends fundamentally on the underlying…

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…

We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…

Optimal transport distances have become a classic tool to compare probability distributions and have found many applications in machine learning. Yet, despite recent algorithmic developments, their complexity prevents their direct use on…

The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…

Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…

Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…

Optimal transport (OT) serves as a natural framework for comparing probability measures, with applications in statistics, machine learning, and applied mathematics. Alas, statistical estimation and exact computation of the OT distances…

Sliced Optimal Transport (OT) simplifies the OT problem in high-dimensional spaces by projecting supports of input measures onto one-dimensional lines and then exploiting the closed-form expression of the univariate OT to reduce the…

Clustering is a fundamental task in the computer vision and machine learning community. Although various methods have been proposed, the performance of existing approaches drops dramatically when handling incomplete high-dimensional data…

Optimal transport (OT) is a powerful geometric tool used to compare and align probability measures following the least effort principle. Despite its widespread use in machine learning (ML), OT problem still bears its computational burden,…

Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently…