Related papers: Minimum cross-entropy distributions on Wasserstein…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
Let $\mu_N$ be the empirical measure associated to a $N$-sample of a given probability distribution $\mu$ on $\mathbb{R}^d$. We are interested in the rate of convergence of $\mu_N$ to $\mu$, when measured in the Wasserstein distance of…
Let $M$ be a connected compact Riemannian manifold possibly with a boundary, let $V\in C^2(M)$ such that $\mu(\d x):=\e^{V(x)}\d x$ is a probability measure, where $\d x$ is the volume measure, and let $L=\Delta+\nabla V$. The exact…
We study the problem of the decentralized computation of entropy-regularized semi-discrete Wasserstein barycenters over a network. Building upon recent primal-dual approaches, we propose a sampling gradient quantization scheme that allows…
K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
Given $m \ge 2$ discrete probability distributions over $n$ states each, the minimum-entropy coupling is the minimum-entropy joint distribution whose marginals are the same as the input distributions. Computing the minimum-entropy coupling…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
We introduce a framework for generating samples of a distribution given a finite number of its moments, targeted to particle-based solutions of kinetic equations and rarefied gas flow simulations. Our model, referred to as the…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
In this paper we study the problem of computing max-entropy distributions over a discrete set of objects subject to observed marginals. Interest in such distributions arises due to their applicability in areas such as statistical physics,…
A robust clustering method for probabilities in Wasserstein space is introduced. This new "trimmed $k$-barycenters" approach relies on recent results on barycenters in Wasserstein space that allow intensive computation, as required by…
This short note is on a property of the $\mathcal{W}_2$ Wasserstein distance which indicates that independent elliptical distributions minimize their $\mathcal{W}_2$ Wasserstein distance from given independent elliptical distributions with…
The Wasserstein distance between probability measures on compact spaces provides a natural invariant quantitative measure of equidistribution, which is partly similar to the classical discrepancy appearing in Erd\"os-Tur\'an type…
Given a collection of probability distributions $p_{1},\ldots,p_{m}$, the minimum entropy coupling is the coupling $X_{1},\ldots,X_{m}$ ($X_{i}\sim p_{i}$) with the smallest entropy $H(X_{1},\ldots,X_{m})$. While this problem is known to be…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…
The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…