Related papers: Quantifying and testing dependence to categorical …
Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation,…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…
Conditional independence (CI) tests underlie many approaches to model testing and structure learning in causal inference. Most existing CI tests for categorical and ordinal data stratify the sample by the conditioning variables, perform…
We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence…
Following our previous work on copula-based nonsymmetric bivariate dependence measures, we propose a new set of conditions on nonsymmetric multivariate dependence measures which characterize both independence and complete dependence of one…
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…
Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…
Hypothesis tests are a crucial statistical tool for data mining and are the workhorse of scientific research in many fields. Here we study differentially private tests of independence between a categorical and a continuous variable. We take…
We propose a test of the conditional independence of random variables $X$ and~$Y$ given~$Z$ under the additional assumption that $X$ is stochastically nondecreasing in~$Z$. The well-documented hardness of testing conditional independence…
In this paper we construct the new coefficient which allows to measure quantitatively the independence of the two discrete random variables. The new inequalities for the matrices with non-negative elements are found
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…
Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…
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 new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson $R^2$ in ANOVA model, the Gini correlation is interpreted as the ratio of the between-group variation and the total…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
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 develops a more general theory of sequences of dependent categorical random variables, extending the works of Korzeniowski (2013) and Traylor (2017) that studied first-kind dependency in sequences of Bernoulli and categorical…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…