Related papers: A Multi-Way Correlation Coefficient
We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for…
Representations of measures of concordance in terms of Pearson' s correlation coefficient are studied. All transforms of random variables are characterized such that the correlation coefficient of the transformed random variables is a…
The two-pion correlation function can be defined as a ratio of either the measured momentum distributions or the normalized momentum space probabilities. We show that the first alternative avoids certain ambiguities since then the…
Similarity distance measure between two trajectories is an essential tool to understand patterns in motion, for example, in Human-Robot Interaction or Imitation Learning. The problem has been faced in many fields, from Signal Processing,…
Pearson's correlation is among the mostly widely reported measures of association. The strength of the statistical evidence for linear association is determined by the p-value of a hypothesis test. If the true distribution of a dataset is…
A margin-free measure of bivariate association generalizing Spearman's rho to the case of non-monotonic dependence is defined in terms of two square integrable functions on the unit interval. Properties of generalized Spearman correlation…
Total correlation (`TC') and dual total correlation (`DTC') are two classical ways to quantify the correlation among an $n$-tuple of random variables. They both reduce to mutual information when $n=2$. The first part of this paper sets up…
Reliably measuring the collinearity of bivariate data is crucial in statistics, particularly for time-series analysis or ongoing studies in which incoming observations can significantly impact current collinearity estimates. Leveraging…
Clustered data are common in practice. Clustering arises when subjects are measured repeatedly, or subjects are nested in groups (e.g., households, schools). It is often of interest to evaluate the correlation between two variables with…
The simplicity of a question such as wondering if correlations characterize or not a certain system collides with the experimental difficulty of accessing such information. Here we present a low demanding experimental approach which refers…
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…
A scheme for characterizing entanglement using the statistical measure of correlation given by the Pearson correlation coefficient (PCC) was recently suggested that has remained unexplored beyond the qubit case. Towards the application of…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
Little attention has been given to the correlation coefficient when data come from discrete or continuous non-normal populations. In this article, we consider the efficiency of two correlation coefficients which are from the same family,…
This paper suggests five measures of association between two random vectors X = (X_1, ..., X_p) and Y = (Y_1, ..., Y_q). They are copula based and therefore invariant with respect to the marginal distributions of the components X_i and Y_j.…
Multiparticle correlations is a hallmark measurement characterizing the behaviour of the assumed Quark Gluon Plasma in heavy ion collisions. In these proceedings an alternative, microscopic approach is resented, based on interacting strings…
The quotient correlation is defined here as an alternative to Pearson's correlation that is more intuitive and flexible in cases where the tail behavior of data is important. It measures nonlinear dependence where the regular correlation…
Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…
Building upon the Chatterjee correlation (2021: J. Am. Stat. Assoc. 116, p2009) for two real-valued variables, this study introduces a generalized measure of directed association between two vector variables, real or complex-valued, and of…
In this paper we consider the fractional parts of a general sequence, for example the sequence $\alpha \sqrt{n}$ or $\alpha n^2$. We give a general method, which allows one to show that long-range correlations (correlations where the…