Related papers: Basic statistics for probabilistic symbolic variab…

This paper presents a factor analysis model for symbolic data, focusing on the particular case of interval-valued variables. The proposed method describes the correlation structure among the measured interval-valued variables in terms of a…

Sums of of 1-dependent integer-valued random variables are approximated by compound Poisson, negative binomial and Binomial distributions and signed compound Poisson measures. Estimates are obtained for total variation and local metrics.…

This paper is concerned by the study of barycenters for random probability measures in the Wasserstein space. Using a duality argument, we give a precise characterization of the population barycenter for various parametric classes of random…

This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a…

A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density…

We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…

A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…

We study a setting where a data holder wishes to share data with a receiver, without revealing certain summary statistics of the data distribution (e.g., mean, standard deviation). It achieves this by passing the data through a…

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several…

We obtain an estimate for the expected subspace robust Wasserstein distance between any probability measure on the unit ball of a separable Hilbert space, and its empirical distribution from $n$ i.i.d. samples.

This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…

The Wasserstein distance quantifies the distance between two probability measures on a metric space. We prove an analogue of the Berry-Esseen inequality for the Wasserstein distance on a finite area hyperbolic surface. This inequality…

Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…

In this work we analyse a number of variants of the Wasserstein distance which allow to focus the classification on the prescribed parts (fragments) of classified 2D curves. These variants are based on the use of a number of discrete…

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,…

The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…

This paper uses sample data to study the problem of comparing populations on finite-dimensional parallelizable Riemannian manifolds and more general trivial vector bundles. Utilizing triviality, our framework represents populations as…

Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport…