Related papers: A Multi-Way Correlation Coefficient
Relatedness is a quantification of how much two human activities are similar in terms of the inputs and contexts needed for their development. Under the idea that it is easier to move between related activities than towards unrelated ones,…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
We show a relation between entanglement and correlations of any form. The internal entanglement of a bipartite system, and its correlations with another system, limit each other. A measure of correlations, of any nature, cannot increase…
Most of the popular dependence measures for two random variables $X$ and $Y$ (such as Pearson's and Spearman's correlation, Kendall's $\tau$ and Gini's $\gamma$) vanish whenever $X$ and $Y$ are independent. However, neither does a vanishing…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
In this review article we consider linear regression analysis from a geometric perspective, looking at standard methods and outputs in terms of the lengths of the relevant vectors and the angles between these vectors. We show that standard…
The article attempts to find an algebraic formula describing the correlation coefficients between random variables and the principal components representing them. As a result of the analysis, starting from selected statistics relating to…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
One obstacle to ``elevating" correlation to causation is the phenomenon of confounding, i.e., when a correlation between two variables exists because both variables are in fact caused by a third variable. The situation where the confounders…
The recent COSY-11 collaboration measurement of the two-proton correlation function in the pp -> ppeta reaction, reported at this meeting [1], arouse some interest in a simple theoretical description of the correlation function. In these…
We give a survey on the concept of Poissonian pair correlation (PPC) of sequences in the unit interval, on existing and recent results and we state a list of open problems. Moreover, we present and discuss a quite recent multi-dimensional…
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…
The kind of information provided by a measurement is determined in terms of the correlation established between observables of the apparatus and the measured system. Using the framework of quantum measurement theory, necessary and…
We provide a method that enables the simple calculation of the maximal correlation coefficient of a bivariate distribution, under suitable conditions. In particular, the method readily applies to known results on order statistics and…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
Correlation function and mutual information are two powerful tools to characterize the correlations in a quantum state of a composite system, widely used in many-body physics and in quantum information science, respectively. We find that…
Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…
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…
We focus on characterizing entanglement of high dimensional bipartite states using various statistical correlators for two-qudit mixed states. The salient results obtained are as follows: (a) A scheme for determining the entanglement…
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We…