Related papers: Detection of Correlated Random Vectors

To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…

Distance correlation is a measure of dependence between two paired random vectors or matrices of arbitrary, not necessarily equal, dimensions. Unlike Pearson correlation, the population distance correlation coefficient is zero if and only…

In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…

In this work, we deal with the relaxation of two central assumptions in standard locally realistic hidden variable (LRHV) inequalities: free will in choosing measurement settings, and the presence of perfect detectors at the measurement…

Results in epidemiology and social science often require the removal of confounding effects from measurements of the pairwise correlation of variables in survey data. This is typically accomplished by some variant of linear regression…

We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…

We study the problem of testing the existence of a dense subhypergraph. The null hypothesis is an Erdos-Renyi uniform random hypergraph and the alternative hypothesis is a uniform random hypergraph that contains a dense subhypergraph. We…

Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…

The maximal correlation coefficient is a well-established generalization of the Pearson correlation coefficient for measuring non-linear dependence between random variables. It is appealing from a theoretical standpoint, satisfying…

In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…

We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…

The hypothesis of randomness is fundamental in statistical machine learning and in many areas of nonparametric statistics; it says that the observations are assumed to be independent and coming from the same unknown probability…

Improving the detection of relevant variables using a new bivariate measure could importantly impact variable selection and large network inference methods. In this paper, we propose a new statistical coefficient that we call the rank…

For $0<q\le 2,\ 1\le k < n,$ let $X=(X_1,...,X_n)$ and $Y=(Y_1,...,Y_n)$ be symmetric $q$-stable random vectors so that the joint distributions of $X_1,...,X_k$ and $X_{k+1},...,X_n$ are equal to the joint distributions of $Y_1,...,Y_k$ and…

Lower bounds for the average probability of error of estimating a hidden variable X given an observation of a correlated random variable Y, and Fano's inequality in particular, play a central role in information theory. In this paper, we…

We consider the classical Neymann-Pearson hypothesis testing problem of signal detection, where under the null hypothesis ($\calH_0$), the received signal is white Gaussian noise, and under the alternative hypothesis ($\calH_1$), the…

Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…

Let $X_N$ be a symmetric $N\times N$ random matrix whose $\sqrt{N}$-scaled centered entries are uniformly square integrable. We prove that if the entries of $X_N$ can be partitioned into independent subsets each of size $o(\log N)$, then…

Let $X$, $Y$ be two correlated discrete random variables. We consider an estimation of $X$ from encoded data $\varphi(Y)$ of $Y$ by some encoder function $\varphi(Y)$. We derive an inequality describing a relation of the correct probability…

This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish…