Related papers: Wasserstein Identity Testing
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…
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…
Considering two random variables with different laws to which we only have access through finite size iid samples, we address how to reweight the first sample so that its empirical distribution converges towards the true law of the second…
In order to adapt the Wasserstein distance to the large sample multivariate non-parametric two-sample problem, making its application computationally feasible, permutation tests based on the Sinkhorn divergence between probability vectors…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
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…
Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely…
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…
We establish conditions to characterize probability measures by their $L^{p}$-quantization error functions in both $\mathbb{R}^{d}$ and Hilbert settings. This characterization is two-fold: static (identity of two distributions) and dynamic…
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…
We study the question of identity testing for structured distributions. More precisely, given samples from a {\em structured} distribution $q$ over $[n]$ and an explicit distribution $p$ over $[n]$, we wish to distinguish whether $q=p$…
This work is motivated by the study of local protein structure, which is defined by two variable dihedral angles that take values from probability distributions on the flat torus. Our goal is to provide the space…
We study the problem of nonparametric two-sample testing using the sliced Wasserstein (SW) distance. While prior theoretical and empirical work indicates that the SW distance offers a promising balance between strong statistical guarantees…
Hypothesis testing for small-sample scenarios is a practically important problem. In this paper, we investigate the robust hypothesis testing problem in a data-driven manner, where we seek the worst-case detector over distributional…
Leveraging the Wasserstein distance -- a summation of sample-wise transport distances in data space -- is advantageous in many applications for measuring support differences between two underlying density functions. However, when supports…
Suppose we are given two metric spaces and a family of continuous transformations from one to the other. Given a probability distribution on each of these two spaces - namely the source and the target measures - the Wasserstein alignment…
In this work we present novel differentially private identity (goodness-of-fit) testers for natural and widely studied classes of multivariate product distributions: Gaussians in $\mathbb{R}^d$ with known covariance and product…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…