Related papers: PT$\mathrm{L}^{p}$: Partial Transport $\mathrm{L}^…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
Collaborative filtering, a widely-used recommendation technique, predicts a user's preference by aggregating the ratings from similar users. As a result, these measures cannot fully utilize the rating information and are not suitable for…
We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a…
Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…
Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…
This paper introduces the first statistically consistent estimator of the optimal transport map between two probability distributions, based on neural networks. Building on theoretical and practical advances in the field of Lipschitz neural…
In this paper, we tackle the transductive semi-supervised learning problem that aims to obtain label predictions for the given unlabeled data points according to Vapnik's principle. Our proposed approach is based on optimal transport, a…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a…
Optimal Transport (OT) theory has seen an increasing amount of attention from the computer science community due to its potency and relevance in modeling and machine learning. It introduces means that serve as powerful ways to compare…
Automatic detection of public transport (PT) usage has important applications for intelligent transport systems. It is crucial for understanding the commuting habits of passengers at large and over longer periods of time. It also enables…
Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…
We consider maps $T$ solving the optimal transport problem with a cost $c(x-y)$ modeled on the $p$-cost. For H\"older continuous marginals, we prove a $C^{1,\alpha}$-partial regularity result for $T $in the set $\{|T(x)-x|>0\}$.
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
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…
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…