Related papers: Inference for Projection-Based Wasserstein Distanc…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
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…
In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such…
We propose a new statistical model, the spiked transport model, which formalizes the assumption that two probability distributions differ only on a low-dimensional subspace. We study the minimax rate of estimation for the Wasserstein…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
We introduce a novel, geometry-aware distance metric for the family of von Mises-Fisher (vMF) distributions, which are fundamental models for directional data on the unit hypersphere. Although the vMF distribution is widely employed in a…
The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of…
Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…
We study the efficacy and efficiency of deep generative networks for approximating probability distributions. We prove that neural networks can transform a low-dimensional source distribution to a distribution that is arbitrarily close to a…
The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common…
Given a cloud of $n$ data points in $\mathbb{R}^d$, consider all projections onto $m$-dimensional subspaces of $\mathbb{R}^d$ and, for each such projection, the empirical distribution of the projected points. What does this collection of…
We use Stein's method to bound the Wasserstein distance of order $2$ between a measure $\nu$ and the Gaussian measure using a stochastic process $(X_t)_{t \geq 0}$ such that $X_t$ is drawn from $\nu$ for any $t > 0$. If the stochastic…
Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…
This article is dedicated to the estimation of Wasserstein distances and Wasserstein costs between two distinct continuous distributions $F$ and $G$ on $\mathbb R$. The estimator is based on the order statistics of (possibly dependent)…
We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and…
In the field of modern high-energy physics research, there is a growing emphasis on utilizing deep learning techniques to optimize event simulation, thereby expanding the statistical sample size for more accurate physical analysis.…
Issued from Optimal Transport, the Wasserstein distance has gained importance in Machine Learning due to its appealing geometrical properties and the increasing availability of efficient approximations. In this work, we consider the problem…
Stein's method has been widely used for probability approximations. However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second- or higher-order…