Related papers: Wasserstein continuity of entropy and outer bounds…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
We study barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we establish absolute continuity of the barycenter of general measures $\Omega \in…
The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
In this paper, we propose a modification to the density approach to Stein's method for intervals for the unit circle $\mathbb{S}^1$ which is motivated by the differing geometry of $\mathbb{S}^1$ to Euclidean space. We provide an upper bound…
In this article, we propose a general framework for the study of differential inclusions in the Wasserstein space of probability measures. Based on earlier geometric insights on the structure of continuity equations, we define solutions of…
We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…
Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied…
While empirical scaling laws for LLM reasoning are well-documented, the theoretical mechanisms governing out-of-distribution (OOD) generalization remain elusive. We formalize reasoning via optimal transport, projecting discrete trajectories…
We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…
We study the non-uniformity of probability measures on the interval and the circle. On the interval, we identify the Wasserstein-$p$ distance with the classical $L^p$-discrepancy. We thereby derive sharp estimates in Wasserstein distances…
Applications of optimal transport have recently gained remarkable attention thanks to the computational advantages of entropic regularization. However, in most situations the Sinkhorn approximation of the Wasserstein distance is replaced by…
The Weinstein operator has several applications in pure and applied Mathematics especially in Fluid Mechanics and satisfies some uncertainty principles similar to the Euclidean Fourier transform. The aim of this paper is establish a…
We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…
Persistent homology offers a powerful tool for extracting hidden topological signals from brain networks. It captures the evolution of topological structures across multiple scales, known as filtrations, thereby revealing topological…
We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $L^1$ Wasserstein distance. We show that measure satisfying certain self-similarity conditions…
A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces…
We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p $\in$ [1, $\infty$) between the empirical measure of independent and identically distributed R d-valued random variables…
Several issues in machine learning and inverse problems require to generate discrete data, as if sampled from a model probability distribution. A common way to do so relies on the construction of a uniform probability distribution over a…