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This work investigates the problem of testing whether $d$ functional random variables are jointly independent using a modified estimator of the $d$-variable Hilbert Schmidt Indepedence Criterion ($d$HSIC) which generalizes HSIC for the case…

Statistics Theory · Mathematics 2022-08-16 Terence Kevin Manfoumbi Djonguet , Guy Martial Nkiet

We develop a Hilbert--Schmidt independence criterion (HSIC)-based framework for testing serial independence in strictly stationary time series. The proposed auto Hilbert--Schmidt independence criterion (AutoHSIC) measures dependence between…

Methodology · Statistics 2026-05-22 Muyi Li , Yuqing Xu , Zhou Zhou

We investigate the problem of testing whether $d$ random variables, which may or may not be continuous, are jointly (or mutually) independent. Our method builds on ideas of the two variable Hilbert-Schmidt independence criterion (HSIC) but…

Statistics Theory · Mathematics 2016-11-07 Niklas Pfister , Peter Bühlmann , Bernhard Schölkopf , Jonas Peters

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data…

Machine Learning · Statistics 2017-09-06 Jakob Runge

A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for…

Machine Learning · Statistics 2014-06-18 Kacper Chwialkowski , Arthur Gretton

Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…

Machine Learning · Statistics 2016-11-03 Adrián Pérez-Suay , Gustau Camps-Valls

Many tools exist to detect dependence between random variables, a core question across a wide range of machine learning, statistical, and scientific endeavors. Although several statistical tests guarantee eventual detection of any…

Machine Learning · Statistics 2026-03-23 Nathaniel Xu , Feng Liu , Danica J. Sutherland

Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly…

Machine Learning · Computer Science 2012-02-20 Kun Zhang , Jonas Peters , Dominik Janzing , Bernhard Schoelkopf

Dette, Siburg, and Stoimenov (2013) introduced a copula-based measure of dependence, which implies independence if it vanishes and is equal to 1 if one variable is a measurable function of the other. For continuous distributions, the…

Statistics Theory · Mathematics 2026-02-17 Mona Azadkia , Holger Dette

We apply the concept of distance covariance for testing independence of two long-range dependent time series. As test statistic we propose a linear combination of empirical distance cross-covariances. We derive the asymptotic distribution…

Statistics Theory · Mathematics 2026-01-28 Annika Betken , Herold Dehling

Quantifying the degree of spatial dependence for linguistic variables is a key task for analyzing dialectal variation. However, existing approaches have important drawbacks. First, they are based on parametric models of dependence, which…

Computation and Language · Computer Science 2016-08-30 Dong Nguyen , Jacob Eisenstein

We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…

Machine Learning · Statistics 2026-02-27 Pouya Roudaki , Shakeel Gavioli-Akilagun , Florian Kalinke , Mona Azadkia , Zoltán Szabó

The paper presents a new copula based method for measuring dependence between random variables. Our approach extends the Maximum Mean Discrepancy to the copula of the joint distribution. We prove that this approach has several advantageous…

Machine Learning · Computer Science 2019-08-15 Barnabas Poczos , Zoubin Ghahramani , Jeff Schneider

We describe a data-efficient, kernel-based approach to statistical testing of conditional independence. A major challenge of conditional independence testing is to obtain the correct test level (the specified upper bound on the rate of…

Machine Learning · Computer Science 2025-09-23 Roman Pogodin , Antonin Schrab , Yazhe Li , Danica J. Sutherland , Arthur Gretton

Kernel-weighted test statistics have been widely used in a variety of settings including non-stationary regression, inference on propensity score and panel data models. We develop the limit theory for a kernel-based specification test of a…

Econometrics · Economics 2023-05-30 Sid Kankanala , Victoria Zinde-Walsh

Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…

Methodology · Statistics 2023-04-19 Yilin Zhang , Songshan Yang

In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is done by defining new types of kernel on an $n$…

Functional Analysis · Mathematics 2024-11-14 Jean Carlo Guella

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

Hilbert-Schmidt independence criterion and distance covariance are methods to describe independence of random variables using either the Kronecker product of positive definite kernels or the Kronecker product of conditionally negative…

Functional Analysis · Mathematics 2022-01-05 Jean Carlo Guella

We consider settings in which the data of interest correspond to pairs of ordered times, e.g, the birth times of the first and second child, the times at which a new user creates an account and makes the first purchase on a website, and the…

Methodology · Statistics 2020-11-19 Tamara Fernández , Wenkai Xu , Marc Ditzhaus , Arthur Gretton