Related papers: A new correlation coefficient, its orthogonal deco…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
Azadkia and Chatterjee (2021) recently introduced a simple nearest neighbor (NN) graph-based correlation coefficient that consistently detects both independence and functional dependence. Specifically, it approximates a measure of…
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 treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
Deheuvels [J. Multivariate Anal. 11 (1981) 102--113] and Genest and R\'{e}millard [Test 13 (2004) 335--369] have shown that powerful rank tests of multivariate independence can be based on combinations of asymptotically independent…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
Given a graph $G$, we consider the model where $G$ is given a random orientation by giving each edge a random direction. It is proven that for $a,b,s\in V(G)$, the events $\{s\to a\}$ and $\{s\to b\}$ are positively correlated. This…
A CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearman's rho in arbitrary dimensions is proposed. Since the new test does not require the existence of any…
Statistical dependence measures like mutual information is ideal for analyzing autoencoders, but it can be ill-posed for deterministic, static, noise-free networks. We adopt the variational (Gaussian) formulation that makes dependence among…
Precise estimation of cross-correlation or similarity between two random variables lies at the heart of signal detection, hyperdimensional computing, associative memories, and neural networks. Although a vast literature exists on different…
In the present paper, we first discuss the Kendall rank correlation coefficient. In continuous case, we define the Kendall rank correlation coefficient in terms of the concomitants of order statistics, find the expected value of the Kendall…
We consider a Hamiltonian $H$ which is the sum of a deterministic part $H_0$ and of a random potential $V$. For finite $N \times N$ matrices, following a method introduced by Kazakov, we derive a representation of the correlation functions…
Identifying how dependence relationships vary across different conditions plays a significant role in many scientific investigations. For example, it is important for the comparison of biological systems to see if relationships between…
In statistical classification and machine learning, as well as in social and other sciences, a number of measures of association have been proposed for assessing and comparing individual classifiers, raters, as well as their groups. In this…
In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
In this paper, we introduce the notion of a ``pairwise independent correlation gap'' for set functions with random elements. The pairwise independent correlation gap is defined as the ratio of the maximum expected value of a set function…
In this paper we propose and study a class of simple, nonparametric, yet interpretable measures of association between two random variables $X$ and $Y$ taking values in general topological spaces. These nonparametric measures -- defined…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…