Related papers: Differential Distance Correlation and Its Applicat…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
Measuring dependence between two random variables is very important, and critical in many applied areas such as variable selection, brain network analysis. However, we do not know what kind of functional relationship is between two…
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…
Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases,…
When two variables are related by a known function, the coefficient of determination (denoted $R^2$) measures the proportion of the total variance in the observations that is explained by that function. This quantifies the strength of the…
Inferring the coupling direction from measured time series of complex systems is challenging. We propose a new state space based causality measure obtained from cross-distance vectors for quantifying interaction strength. It is a model-free…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
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…
The model for homogeneity of proportions in a two-way contingency-table/cross-tabulation is the same as the model of independence, except that the probabilistic process generating the data is viewed as fixing the column totals (but not the…
Variable screening has been a useful research area that deals with ultrahigh-dimensional data. When there exist both marginally and jointly dependent predictors to the response, existing methods such as conditional screening or iterative…
Through computer simulations, we research several different measures of dependence, including Pearson's and Spearman's correlation coefficients, the maximal correlation, the distance correlation, a function of the mutual information called…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
We describe a novel non-parametric statistical hypothesis test of relative dependence between a source variable and two candidate target variables. Such a test enables us to determine whether one source variable is significantly more…
In this paper, we investigate the problem of deciding whether two standard normal random vectors $\mathsf{X}\in\mathbb{R}^{n}$ and $\mathsf{Y}\in\mathbb{R}^{n}$ are correlated or not. This is formulated as a hypothesis testing problem,…
In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…
Reliable measurement of dependence between variables is essential in many applications of statistics and machine learning. Current approaches for dependence estimation, especially density-based approaches, lack in precision, robustness…
The need to test whether two random vectors are independent has spawned a large number of competing measures of dependence. We are interested in nonparametric measures that are invariant under strictly increasing transformations, such as…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
The conditional randomization test (CRT) was recently proposed to test whether two random variables X and Y are conditionally independent given random variables Z. The CRT assumes that the conditional distribution of X given Z is known…
Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…