Related papers: Asymptotic Distribution-Free Independence Test for…

Symmetry plays a central role in the sciences, machine learning, and statistics. For situations in which data are known to obey a symmetry, a multitude of methods that exploit symmetry have been developed. Statistical tests for the presence…

Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…

We propose a nonparametric test for serial independence that aggregates pairwise similarities of observations with lag-dependent weights. The resulting statistic is powerful to general forms of temporal dependence, including nonlinear and…

We provide a unified framework for independence and mean independence tests based on the Hilbert-Schmidt independence criterion, extending some previous results in the literature to hold in general topological spaces. We also present a…

We propose a methodology for testing linear hypothesis in high-dimensional linear models. The proposed test does not impose any restriction on the size of the model, i.e. model sparsity or the loading vector representing the hypothesis.…

We introduce an independence criterion based on entropy regularized optimal transport. Our criterion can be used to test for independence between two samples. We establish non-asymptotic bounds for our test statistic and study its…

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…

Given a random sample of size $n$ from a $p$ dimensional random vector, where both $n$ and $p$ are large, we are interested in testing whether the $p$ components of the random vector are mutually independent. This is the so-called complete…

In many real-world scenarios, interested variables are often represented as discretized values due to measurement limitations. Applying Conditional Independence (CI) tests directly to such discretized data, however, can lead to incorrect…

Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…

This paper takes a different look on the problem of testing the mutual independence of the components of a high-dimensional vector. Instead of testing if all pairwise associations (e.g. all pairwise Kendall's $\tau$) between the components…

We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when $P(X \mid Y, Z) = P(X \mid Y)$, $Z$ is not useful as a feature to predict $X$,…

We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach, which we call MINT, is based on the estimation of mutual information, whose decomposition into joint and…

We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters, and can…

Many relations of scientific interest are nonlinear, and even in linear systems distributions are often non-Gaussian, for example in fMRI BOLD data. A class of search procedures for causal relations in high dimensional data relies on sample…

This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of…

In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…

When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…

We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…