Related papers: Kernel-based Tests for Joint Independence
A simple and intuitive method for feature selection consists of choosing the feature subset that maximizes a nonparametric measure of dependence between the response and the features. A popular proposal from the literature uses the…
Measuring conditional independence is one of the important tasks in statistical inference and is fundamental in causal discovery, feature selection, dimensionality reduction, Bayesian network learning, and others. In this work, we explore…
A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive…
Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…
We discuss how MultiFIT, the Multiscale Fisher's Independence Test for Multivariate Dependence proposed by Gorsky and Ma (2022), compares to existing linear-time kernel tests based on the Hilbert-Schmidt independence criterion (HSIC). We…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general…
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches…
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 propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test…
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…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
We propose a novel statistical test to assess the mutual independence of multidimensional random vectors. Our approach is based on the $L_1$-distance between the joint density function and the product of the marginal densities associated…
We consider a linear regression model and propose an omnibus test to simultaneously check the assumption of independence between the error and the predictor variables, and the goodness-of-fit of the parametric model. Our approach is based…
Evaluation of statistical dependencies between two data samples is a basic problem of data science/machine learning, and HSIC (Hilbert-Schmidt Information Criterion)~\cite{HSIC} is considered the state-of-art method. However, for size $n$…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
We propose an estimator of the Hilbert-Schmidt Independence Criterion obtained from an appropriate modification of the usual estimator. We then get asymptotic normality of this estimator both under independence hypothesis and under the…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…