English
Related papers

Related papers: Distance and Kernel-Based Measures for Global and …

200 papers

In this paper we introduce a new measure of conditional dependence between two random vectors ${\boldsymbol X}$ and ${\boldsymbol Y}$ given another random vector $\boldsymbol Z$ using the ball divergence. Our measure characterizes…

Statistics Theory · Mathematics 2024-08-01 Bilol Banerjee , Bhaswar B. Bhattacharya , Anil K. Ghosh

Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that…

Machine Learning · Statistics 2017-11-07 Ho Chung Leon Law , Christopher Yau , Dino Sejdinovic

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…

Statistics Theory · Mathematics 2008-12-18 Bruce G. Lindsay , Marianthi Markatou , Surajit Ray , Ke Yang , Shu-Chuan Chen

We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to determine whether two collections of samples follow the same distribution. To address this, we propose a novel framework…

Machine Learning · Statistics 2024-12-23 Jie Wang , Santanu S. Dey , Yao Xie

The distribution closeness testing (DCT) assesses whether the distance between a distribution pair is at least $\epsilon$-far. Existing DCT methods mainly measure discrepancies between a distribution pair defined on discrete one-dimensional…

Machine Learning · Computer Science 2025-10-10 Zhijian Zhou , Liuhua Peng , Xunye Tian , Feng Liu

This paper is concerned with testing normality in a Hilbert space based on the maximum mean discrepancy. Specifically, we discuss the behavior of the test from two standpoints: asymptotics and practical aspects. Asymptotic normality of the…

Statistics Theory · Mathematics 2019-02-12 Natsumi Makigusa , Kanta Naito

We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…

Machine Learning · Computer Science 2016-07-26 Francesco Solera , Andrea Palazzi

We study the comparison problem of distribution equality between two random samples under a right censoring scheme. To address this problem, we design a series of tests based on energy distance and kernel mean embeddings. We calibrate our…

Methodology · Statistics 2019-12-10 Marcos Matabuena , Oscar Hernan Madrid Padilla

We propose a class of nonparametric two-sample tests with a cost linear in the sample size. Two tests are given, both based on an ensemble of distances between analytic functions representing each of the distributions. The first test uses…

Machine Learning · Statistics 2015-06-16 Kacper Chwialkowski , Aaditya Ramdas , Dino Sejdinovic , Arthur Gretton

We propose a framework to construct practical kernel-based two-sample tests from the family of $f$-divergences. The test statistic is computed from the witness function of a regularized variational representation of the divergence, which we…

Machine Learning · Statistics 2026-01-28 Mónica Ribero , Antonin Schrab , Arthur Gretton

This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only…

Machine Learning · Statistics 2021-10-01 Srinjoy Das , Hrushikesh Mhaskar , Alexander Cloninger

Out-of-distribution generalization is key to building models that remain reliable across diverse environments. Recent causality-based methods address this challenge by learning invariant causal relationships in the underlying…

Statistics Theory · Mathematics 2025-10-24 Théotime Le Goff , Émilie Devijver

The kernel Maximum Mean Discrepancy~(MMD) is a popular multivariate distance metric between distributions that has found utility in two-sample testing. The usual kernel-MMD test statistic is a degenerate U-statistic under the null, and thus…

Methodology · Statistics 2025-09-16 Shubhanshu Shekhar , Ilmun Kim , Aaditya Ramdas

Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…

Maximum mean discrepancies (MMDs) like the kernel Stein discrepancy (KSD) have grown central to a wide range of applications, including hypothesis testing, sampler selection, distribution approximation, and variational inference. In each…

Machine Learning · Statistics 2025-03-26 Alessandro Barp , Carl-Johann Simon-Gabriel , Mark Girolami , Lester Mackey

Modern kernel-based two-sample tests have shown great success in distinguishing complex, high-dimensional distributions with appropriate learned kernels. Previous work has demonstrated that this kernel learning procedure succeeds, assuming…

Machine Learning · Statistics 2022-01-06 Feng Liu , Wenkai Xu , Jie Lu , Danica J. Sutherland

To adapt kernel two-sample and independence testing to complex structured data, aggregation of multiple kernels is frequently employed to boost testing power compared to single-kernel tests. However, we observe a phenomenon that directly…

Machine Learning · Computer Science 2025-10-14 Zhijian Zhou , Xunye Tian , Liuhua Peng , Chao Lei , Antonin Schrab , Danica J. Sutherland , Feng Liu

Nonparametric two sample or homogeneity testing is a decision theoretic problem that involves identifying differences between two random variables without making parametric assumptions about their underlying distributions. The literature is…

Statistics Theory · Mathematics 2015-10-14 Aaditya Ramdas , Nicolas Garcia , Marco Cuturi

Machine learning and deep learning have been used extensively to classify physical surfaces through images and time-series contact data. However, these methods rely on human expertise and entail the time-consuming processes of data and…

Machine Learning · Computer Science 2023-08-10 Behnam Khojasteh , Friedrich Solowjow , Sebastian Trimpe , Katherine J. Kuchenbecker

Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…

Methodology · Statistics 2023-07-31 Hoseung Song , Michael C. Wu