Related papers: Fast Regularized Discrete Optimal Transport with G…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
In many real-world settings--e.g., single-cell RNA sequencing, mobility sensing, and environmental monitoring--data are observed only as temporally aggregated snapshots collected over finite time windows, often with noisy or uncertain…
Alignment plays a fundamental role in many machine learning problems, such as multi-network analysis, multimodal learning, and point cloud registration. Recent works increasingly leverage optimal transport (OT) for distributional alignment,…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Defining meaningful distances between samples in a dataset is a fundamental problem in machine learning. Optimal Transport (OT) lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples.…
Transportation of samples across different domains is a central task in several machine learning problems. A sensible requirement for domain transfer tasks in computer vision and language domains is the sparsity of the transportation map,…
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…
Over-parameterized deep neural networks trained by simple first-order methods are known to be able to fit any labeling of data. Such over-fitting ability hinders generalization when mislabeled training examples are present. On the other…
We present rectified flow, a surprisingly simple approach to learning (neural) ordinary differential equation (ODE) models to transport between two empirically observed distributions \pi_0 and \pi_1, hence providing a unified solution to…
Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…
We address the computational and theoretical limitations of current distributional alignment methods for source-free unsupervised domain adaptation (SFUDA) using source class-mean features. In particular, we focus on estimating…
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…
Distributed optimization problems usually face inexact communication issues induced by channel noise, communication quantization or differential privacy protection. Most existing algorithms need a two-timescale setting of the stepsize of…
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…
This paper addresses an Optimal Transport (OT)-based efficient multi-robot exploration problem, considering the energy constraints of a multi-robot system. The efficiency in this problem implies how a team of robots (agents) covers a given…
Domain adaptation aims to transfer knowledge of labeled instances obtained from a source domain to a target domain to fill the gap between the domains. Most domain adaptation methods assume that the source and target domains have the same…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
We study finite-sample statistical performance guarantees for distributionally robust optimization (DRO) with optimal transport (OT) and OT-regularized divergence model neighborhoods. Specifically, we derive concentration inequalities for…
Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…
Sorting an array is a fundamental routine in machine learning, one that is used to compute rank-based statistics, cumulative distribution functions (CDFs), quantiles, or to select closest neighbors and labels. The sorting function is…