Related papers: Partial Distance Correlation with Methods for Diss…
Distance covariance is a widely used statistical methodology for testing the dependency between two groups of variables. Despite the appealing properties of consistency and superior testing power, the testing results of distance covariance…
We consider the problem of calculating distance correlation coefficients between random vectors whose joint distributions belong to the class of Lancaster distributions. We derive under mild convergence conditions a general series…
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…
Covariance is used as an inner product on a formal vector space built on n random variables to define measures of correlation Md across a set of vectors in a d-dimensional space. For d = 1, one has the diameter; for d = 2, one has an area.…
Distance covariance is a popular dependence measure for two random vectors $X$ and $Y$ of possibly different dimensions and types. Recent years have witnessed concentrated efforts in the literature to understand the distributional…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…
The correlation distance quantifies the statistical independence of two classical or quantum systems, via the distance from their joint state to the product of the marginal states. Tight lower bounds are given for the mutual information…
Classical dependence measures such as Pearson correlation, Spearman's $\rho$, and Kendall's $\tau$ can detect only monotonic or linear dependence. To overcome these limitations, Szekely et al.(2007) proposed distance covariance as a…
Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not),…
Regression is one of the most fundamental statistical inference problems. A broad definition of regression problems is as estimation of the distribution of an outcome using a family of probability models indexed by covariates. Despite the…
The aim of this thesis is to find a solution to the non-parametric independence problem in separable metric spaces. Suppose we are given finite collection of samples from an i.i.d. sequence of paired random elements, where each marginal has…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
Distance correlation coefficient (DCC) can be used to identify new associations and correlations between multiple variables. The distance correlation coefficient applies to variables of any dimension, can be used to determine smaller sets…
Sz\'{e}kely, Rizzo and Bakirov (Ann. Statist. 35 (2007) 2769-2794) and Sz\'{e}kely and Rizzo (Ann. Appl. Statist. 3 (2009) 1236-1265), in two seminal papers, introduced the powerful concept of distance correlation as a measure of dependence…
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…
In this paper we explore partial coherence as a tool for evaluating causal influence of one signal sequence on another. In some cases the signal sequence is sampled from a time- or space-series. The key idea is to establish a connection…
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…