Related papers: Optimal transport distances to characterise electr…

Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…

Detecting Out-of-Distribution (OOD) inputs is crucial for improving the reliability of deep neural networks in the real-world deployment. In this paper, inspired by the inherent distribution shift between ID and OOD data, we propose a novel…

We present several algorithms designed to learn a pattern of correspondence between two data sets in situations where it is desirable to match elements that exhibit a relationship belonging to a known parametric model. In the motivating…

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…

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…

The current best practice for computing optimal transport (OT) is via entropy regularization and Sinkhorn iterations. This algorithm runs in quadratic time as it requires the full pairwise cost matrix, which is prohibitively expensive for…

We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard differentiability analysis of EOT potentials with respect to…

This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…

Recent advances in label assignment in object detection mainly seek to independently define positive/negative training samples for each ground-truth (gt) object. In this paper, we innovatively revisit the label assignment from a global…

We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction…

We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove…

Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…

Semantically coherent out-of-distribution (SCOOD) detection aims to discern outliers from the intended data distribution with access to unlabeled extra set. The coexistence of in-distribution and out-of-distribution samples will exacerbate…

Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…

We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…

We propose a method to identify and characterize distribution shifts in classification datasets based on optimal transport. It allows the user to identify the extent to which each class is affected by the shift, and retrieves corresponding…

Machine learning (ML) techniques have recently enabled enormous gains in sensitivity to new phenomena across the sciences. In particle physics, much of this progress has relied on excellent simulations of a wide range of physical processes.…

In this paper, we consider Strassen's version of optimal transport (OT) problem, which concerns minimizing the excess-cost probability (i.e., the probability that the cost is larger than a given value) over all couplings of two given…

The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…

Imitation learning algorithms have been interpreted as variants of divergence minimization problems. The ability to compare occupancy measures between experts and learners is crucial in their effectiveness in learning from demonstrations.…