Distance correlation ≈ Distance correlation
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Correlation Coefficients: Appropriate Use and Interpretation Open
Correlation in the broadest sense is a measure of an association between variables. In correlated data, the change in the magnitude of 1 variable is associated with a change in the magnitude of another variable, either in the same (positiv…
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On relationships between the Pearson and the distance correlation coefficients Open
In this paper we show that for any fixed Pearson correlation coefficient strictly between −1 and 1, the distance correlation coefficient can take any value in the open unit interval (0,1).
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Dependent Evidence Combination Based on Shearman Coefficient and Pearson Coefficient Open
Dempster-Shafer evidence theory is efficient to deal with uncertain information. One assumption of evidence theory is that the source of information should be independent when combined by Dempster's rule for evidence combination. However, …
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Biostatistics series module 6: Correlation and linear regression Open
Correlation and linear regression are the most commonly used techniques for quantifying the association between two numeric variables. Correlation quantifies the strength of the linear relationship between paired variables, expressing this…
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Correlation and agreement: overview and clarification of competing concepts and measures. Open
Agreement and correlation are widely-used concepts that assess the association between variables. Although similar and related, they represent completely different notions of association. Assessing agreement between variables assumes that …
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Conditional Distance Correlation Open
Statistical inference on conditional dependence is essential in many fields including genetic association studies and graphical models. The classic measures focus on linear conditional correlations and are incapable of characterizing nonli…
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Myths About Linear and Monotonic Associations: Pearson’s <i>r</i>, Spearman’s <i>ρ</i>, and Kendall’s <i>τ</i> Open
Pearson’s correlation coefficient is considered a measure of linear association between bivariate random variables X and Y. It is recommended not to use it for other forms of associations. Indeed, for nonlinear monotonic associations alter…
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Robust Permutation Tests For Correlation And Regression Coefficients Open
Given a sample from a bivariate distribution, consider the problem of testing independence. A permutation test based on the sample correlation is known to be an exact level α test. However, when used to test the null hypothesis that the sa…
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The Chi-Square Test of Distance Correlation Open
Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any t…
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Robust Jet Classifiers through Distance Correlation Open
While deep learning has proven to be extremely successful at supervised classification tasks at the LHC and beyond, for practical applications, raw classification accuracy is often not the only consideration. One crucial issue is the stabi…
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Ball Covariance: A Generic Measure of Dependence in Banach Space Open
Technological advances in science and engineering have led to the routine collection of large and complex data objects, where the dependence structure among those objects is often of great interest. Those complex objects (e.g., different b…
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Applications of distance correlation to time series Open
The use of empirical characteristic functions for inference problems, including estimation in some special parametric settings and testing for goodness of fit, has a long history dating back to the 70s. More recently, there has been renewe…
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New improvements in the use of dependence measures for sensitivity analysis and screening Open
Physical phenomena are commonly modeled by numerical simulators. Such codes\ncan take as input a high number of uncertain parameters and it is important to\nidentify their influences via a global sensitivity analysis (GSA). However,\nthese…
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On Clustering Time Series Using Euclidean Distance and Pearson\n Correlation Open
For time series comparisons, it has often been observed that z-score\nnormalized Euclidean distances far outperform the unnormalized variant. In this\npaper we show that a z-score normalized, squared Euclidean Distance is, in\nfact, equal …
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A new framework for distance and kernel-based metrics in high dimensions Open
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot …
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Correlation Coefficients for a Study with Repeated Measures Open
Repeated measures are increasingly collected in a study to investigate the trajectory of measures over time. One of the first research questions is to determine the correlation between two measures. The following five methods for correlati…
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Configuration model for correlation matrices preserving the node strength Open
Correlation matrices are a major type of multivariate data. To examine properties of a given correlation matrix, a common practice is to compare the same quantity between the original correlation matrix and reference correlation matrices, …
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A Statistically and Numerically Efficient Independence Test Based on Random Projections and Distance Covariance Open
Testing for independence plays a fundamental role in many statistical techniques. Among the nonparametric approaches, the distance-based methods (such as the distance correlation-based hypotheses testing for independence) have many advanta…
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Distance multivariance: New dependence measures for random vectors Open
We introduce two new measures for the dependence of $n\\ge2$ random variables: distance multivariance and total distance multivariance. Both measures are based on the weighted $L^{2}$-distance of quantities related to the characteristic fu…
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On Clustering Time Series Using Euclidean Distance and Pearson Correlation Open
For time series comparisons, it has often been observed that z-score normalized Euclidean distances far outperform the unnormalized variant. In this paper we show that a z-score normalized, squared Euclidean Distance is, in fact, equal to …
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Distance Correlation-Based Feature Selection in Random Forest Open
The Pearson correlation coefficient (ρ) is a commonly used measure of correlation, but it has limitations as it only measures the linear relationship between two numerical variables. The distance correlation measures all types of dependenc…
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Multiple-to-multiple path analysis model Open
One-to-multiple path analysis model describes the regulation mechanism of multiple independent variables to one dependent variable by dividing the correlation coefficient and the determination coefficient. How to analyse more complex regul…
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Optimizing age of information with correlated sources Open
We develop a simple model for the timely monitoring of correlated sources over a wireless network. Using this model, we study how to optimize weighted-sum average Age of Information (AoI) in the presence of correlation. First, we discuss h…
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Quantifying the Informativeness of Similarity Measurements Open
In this paper, we describe an unsupervised measure for quantifying the `informativeness' of correlation matrices formed from the pairwise similarities or relationships among data instances. The measure quantifies the heterogeneity of the c…
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Estimating Feature-Label Dependence Using Gini Distance Statistics Open
Identifying statistical dependence between the features and the label is a fundamental problem in supervised learning. This paper presents a framework for estimating dependence between numerical features and a categorical label using gener…
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Local Canonical Correlation Analysis for Nonlinear Common Variables Discovery Open
In this paper, we address the problem of hidden common variables discovery\nfrom multimodal data sets of nonlinear high-dimensional observations. We\npresent a metric based on local applications of canonical correlation analysis\n(CCA) and…
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Distance canonical correlation analysis with application to an imaging-genetic study Open
Distance correlation is a measure that can detect both linear and nonlinear associations. However, applying distance correlation to imaging genetic studies often needs multiple testing correction due to the large number of multiple inferen…
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Maximal Correlation Regression Open
In this paper, we propose a novel regression analysis approach, called maximal correlation regression, by exploiting the ideas from the Hirschfeld-Gebelein-Rényi (HGR) maximal correlation. We show that in supervised learning problems, the …
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Detecting independence of random vectors: generalized distance covariance and Gaussian covariance Open
Distance covariance is a quantity to measure the dependence of two random vectors. We show that the original concept introduced and developed by Székely, Rizzo and Bakirov can be embedded into a more general framework based on symmetric Lé…
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An information network flow approach for measuring functional connectivity and predicting behavior Open
Introduction Connectome‐based predictive modeling (CPM) is a recently developed machine‐learning‐based framework to predict individual differences in behavior from functional brain connectivity (FC). In these models, FC was operationalized…