Related papers: Statistical dependence: Beyond Pearson's $\rho$
Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…
Understanding and developing a correlation measure that can detect general dependencies is not only imperative to statistics and machine learning, but also crucial to general scientific discovery in the big data age. In this paper, we…
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…
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…
Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for…
The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalisation of classical measures of linear dependence (such as the covariance) not…
In this article, we show that the recently introduced ordinal pattern dependence fits into the axiomatic framework of general multivariate dependence measures, i.e., measures of dependence between two multivariate random objects.…
In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular…
It is well known that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial…
The concept of independence plays a crucial role in probability theory and has been the subject of extensive research in recent years. Numerous approaches have been proposed to test for independence; however, most of them address the…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these…
The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the…
We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…
Let X_n=(x_{ij}) be an n by p data matrix, where the n rows form a random sample of size n from a certain p-dimensional population distribution. Let R_n=(\rho_{ij}) be the p\times p sample correlation matrix of X_n; that is, the entry…
A new index based on empirical copulas, termed the Copula Statistic (CoS), is introduced for assessing the strength of multivariate dependence and for testing statistical independence. New properties of the copulas are proved. They allow us…
Categorical variables are of uttermost importance in biomedical research. When two of them are considered, it is often the case that one wants to test whether or not they are statistically dependent. We show weaknesses of classical methods…
Measuring and quantifying dependencies between random variables (RV's) can give critical insights into a data-set. Typical questions are: `Do underlying relationships exist?', `Are some variables redundant?', and `Is some target variable…
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…
The Pearson-Matthews correlation coefficient (usually abbreviated MCC) is considered to be one of the most useful metrics for the performance of a binary classification or hypothesis testing method (for the sake of conciseness we will use…
The dependencies of the lagged (Pearson) correlation function on the coefficients of multivariate autoregressive models are interpreted in the framework of time series graphs. Time series graphs are related to the concept of Granger…