Related papers: Kernel-based independence and mean independence te…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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 $n$…
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…
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…
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…