Related papers: Wasserstein Identity Testing
Consider the empirical measure, $\hat{\mathbb{P}}_N$, associated to $N$ i.i.d. samples of a given probability distribution $\mathbb{P}$ on the unit interval. For fixed $\mathbb{P}$ the Wasserstein distance between $\hat{\mathbb{P}}_N$ and…
In the study of dynamical and physical systems, the input parameters are often uncertain or randomly distributed according to a measure $\varrho$. The system's response $f$ pushes forward $\varrho$ to a new measure $f\circ \varrho$ which we…
Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…
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…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
The smooth 1-Wasserstein distance (SWD) $W_1^\sigma$ was recently proposed as a means to mitigate the curse of dimensionality in empirical approximation while preserving the Wasserstein structure. Indeed, SWD exhibits parametric convergence…
Testing whether the observed data conforms to a purported model (probability distribution) is a basic and fundamental statistical task, and one that is by now well understood. However, the standard formulation, identity testing, fails to…
The emergence of time-series foundation model research elevates the growing need to measure the (dis)similarity of time-series datasets. A time-series dataset similarity measure aids research in multiple ways, including model selection,…
We investigate the problem of identity testing for multidimensional histogram distributions. A distribution $p: D \rightarrow \mathbb{R}_+$, where $D \subseteq \mathbb{R}^d$, is called a $k$-histogram if there exists a partition of the…
In this paper, we use the class of Wasserstein metrics to study asymptotic properties of posterior distributions. Our first goal is to provide sufficient conditions for posterior consistency. In addition to the well-known Schwartz's…
We obtain explicit $p$-Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically…
The empirical Wasserstein projection (WP) distance quantifies the Wasserstein distance from the empirical distribution to a set of probability measures satisfying given expectation constraints. The WP is a powerful tool because it mitigates…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wasserstein (WoW) distance is a powerful, but computationally…
Change point detection for time series analysis is a difficult and important problem in applied statistics, for which a variety of approaches have been developed in the past several decades. Here, the Wasserstein metric is employed as a…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
Computing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various applied fields. However, the practical applicability of these…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
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…