Related papers: On parameter estimation with the Wasserstein dista…

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…

In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…

While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…

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…

This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…

We study the problem of distributional matrix completion: Given a sparsely observed matrix of empirical distributions, we seek to impute the true distributions associated with both observed and unobserved matrix entries. This is a…

We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…

Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…

Random probabilities are a key component to many nonparametric methods in Statistics and Machine Learning. To quantify comparisons between different laws of random probabilities several works are starting to use the elegant Wasserstein over…

In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in the framework of Symbolic Data Analysis and the parameters of the model are…

Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…

Parameter estimation is a fundamental challenge in machine learning, crucial for tasks such as neural network weight fitting and Bayesian inference. This paper focuses on the complexity of estimating translation $\boldsymbol{\mu} \in…

Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric…

We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method…

Squared Wasserstein distance is a frequently used tool to measure discrepancy between probability distributions. This distance is typically computed between empirical measures of size $n$ from two underlying random samples. Unfortunately,…

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of…

This paper derives non-asymptotic error bounds for nonlinear stochastic approximation algorithms in the Wasserstein-$p$ distance. To obtain explicit finite-sample guarantees for the last iterate, we develop a coupling argument that compares…

The autocovariance and cross-covariance functions naturally appear in many time series procedures (e.g., autoregression or prediction). Under assumptions, empirical versions of the autocovariance and cross-covariance are asymptotically…

We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract…

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…