Related papers: Minibatch optimal transport distances; analysis an…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
This article is an exposition on some recent theoretical advances in learning latent structured models, with a primary focus on the fundamental roles that optimal transport distances play in the statistical theory. We aim at what may be the…
Comparing probability distributions is a fundamental problem in data sciences. Simple norms and divergences such as the total variation and the relative entropy only compare densities in a point-wise manner and fail to capture the geometric…
Few-Shot classification aims at solving problems that only a few samples are available in the training process. Due to the lack of samples, researchers generally employ a set of training tasks from other domains to assist the target task,…
We introduce an efficient framework for computing the distance between collider events using the tools of Linearized Optimal Transport (LOT). This preserves many of the advantages of the recently-introduced Energy Mover's Distance, which…
Optimal transport (OT) is a popular measure to compare probability distributions. However, OT suffers a few drawbacks such as (i) a high complexity for computation, (ii) indefiniteness which limits its applicability to kernel machines. In…
Discrete flow matching, a recent framework for modeling categorical data, has shown competitive performance with autoregressive models. However, unlike continuous flow matching, the rectification strategy cannot be applied due to the…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…
We investigate finding a map $g$ within a function class $G$ that minimises an Optimal Transport (OT) cost between a target measure $\nu$ and the image by $g$ of a source measure $\mu$. This is relevant when an OT map from $\mu$ to $\nu$…
Distributed distribution comparison aims to measure the distance between the distributions whose data are scattered across different agents in a distributed system and cannot even be shared directly among the agents. In this study, we…
Optimal transport (OT) has become a widely used tool in the machine learning field to measure the discrepancy between probability distributions. For instance, OT is a popular loss function that quantifies the discrepancy between an…
We study the fundamental computational problem of approximating optimal transport (OT) equations using neural differential equations (Neural ODEs). More specifically, we develop a novel framework for approximating unbalanced optimal…
Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
Deep learning classifiers are now known to have flaws in the representations of their class. Adversarial attacks can find a human-imperceptible perturbation for a given image that will mislead a trained model. The most effective methods to…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
The discretization of optimal transport problems often leads to large linear programs with sparse solutions. We derive error estimates for the approximation of the problem using convex combinations of Dirac measures and devise an active-set…
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,…