English
Related papers

Related papers: Two-sample tests for relevant differences in persi…

200 papers

We propose a study of a distribution registration model for general deformation functions. In this framework, we provide estimators of the deformations as well as a goodness of fit test of the model. For this, we consider a criterion which…

Statistics Theory · Mathematics 2015-10-02 Eustasio Del Barrio , Hélène Lescornel , Jean-Michel Loubes

We study the perturbation of a measure $\mu \in \mathscr{P}(\mathbb{R})$ consisting in superposing two copies of $\mu$, each slightly shifted by a small distance $\pm h$. The difference between $\mu$ and its perturbation is measured with a…

Optimization and Control · Mathematics 2026-03-03 Averil Aussedat

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…

Machine Learning · Computer Science 2025-11-18 Cheongjae Jang , Jonghyun Won , Soyeon Jun , Chun Kee Chung , Keehyoung Joo , Yung-Kyun Noh

The goal of two-sample tests is to assess whether two samples, $S_P \sim P^n$ and $S_Q \sim Q^m$, are drawn from the same distribution. Perhaps intriguingly, one relatively unexplored method to build two-sample tests is the use of binary…

Machine Learning · Statistics 2018-03-14 David Lopez-Paz , Maxime Oquab

In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…

Methodology · Statistics 2024-10-08 Bilol Banerjee

This paper addresses the multiple two-sample test problem in a graph-structured setting, which is a common scenario in fields such as Spatial Statistics and Neuroscience. Each node $v$ in fixed graph deals with a two-sample testing problem…

Machine Learning · Statistics 2024-02-09 Alejandro de la Concha , Nicolas Vayatis , Argyris Kalogeratos

We study the problem of two-sample comparison with categorical data when the contingency table is sparsely populated. In modern applications, the number of categories is often comparable to the sample size, causing existing methods to have…

Methodology · Statistics 2014-08-14 Hao Chen , Nancy R. Zhang

In this paper, we propose novel, fully Bayesian non-parametric tests for one-sample and two-sample multivariate location problems. We model the underlying distribution using a Dirichlet process prior, and develop a testing procedure based…

Statistics Theory · Mathematics 2021-08-03 Indrabati Bhattacharya , Subhashis Ghosal

Topological Data Analysis (TDA) provides a toolkit for the study of the shape of high dimensional and complex data. While operating on a space of persistence diagrams is cumbersome, persistence norms provide a simple real value measure of…

Methodology · Statistics 2023-09-26 Pawel Dlotko , Simon Rudkin

Randomly censored survival data are frequently encountered in applied sciences including biomedical or reliability applications and clinical trial analyses. Testing the significance of statistical hypotheses is crucial in such analyses to…

Methodology · Statistics 2019-01-08 Abhik Ghosh , Ayanendranath Basu , Leandro Pardo

This paper presents a computational framework for the concise encoding of an ensemble of persistence diagrams, in the form of weighted Wasserstein barycenters [100], [102] of a dictionary of atom diagrams. We introduce a multi-scale…

Machine Learning · Computer Science 2023-09-18 Keanu Sisouk , Julie Delon , Julien Tierny

The paper introduces a new kernel-based Maximum Mean Discrepancy (MMD) statistic for measuring the distance between two distributions given finitely-many multivariate samples. When the distributions are locally low-dimensional, the proposed…

Machine Learning · Statistics 2018-09-03 Xiuyuan Cheng , Alexander Cloninger , Ronald R. Coifman

We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance--covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance…

Statistics Theory · Mathematics 2012-06-06 Jun Li , Song Xi Chen

This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the…

Machine Learning · Computer Science 2026-01-22 Keanu Sisouk , Eloi Tanguy , Julie Delon , Julien Tierny

We propose an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. that two histograms are drawn from the same distribution). The…

Data Analysis, Statistics and Probability · Physics 2013-05-22 Sergey Bityukov , Nikolai Krasnikov , Alexander Nikitenko , Vera Smirnova

In this paper, change-point problems for long memory stochastic volatility models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting…

Statistics Theory · Mathematics 2017-06-21 Annika Betken , Rafał Kulik

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…

Probability · Mathematics 2020-02-20 Yating Liu , Gilles Pagès

The deviation test belong to core tools in point process statistics, where hypotheses are typically tested considering differences between an empirical summary function and its expectation under the null hypothesis, which depend on a…

Methodology · Statistics 2015-03-13 Mari Myllymäki , Pavel Grabarnik , Henri Seijo , Dietrich Stoyan

Motivated by the increasing use of kernel-based metrics for high-dimensional and large-scale data, we study the asymptotic behavior of kernel two-sample tests when the dimension and sample sizes both diverge to infinity. We focus on the…

Statistics Theory · Mathematics 2024-10-31 Jian Yan , Xianyang Zhang

In this article we propose a novel approach for comparing the persistent homology representations of two spaces (filtrations). Commonly used methods are based on numerical summaries such as persistence diagrams and persistence landscapes,…

Machine Learning · Computer Science 2021-01-05 Yohai Reani , Omer Bobrowski