Related papers: A new Gini correlation between quantitative and qu…
The Gini index underestimates inequality for heavy-tailed distributions: for example, a Pareto distribution with exponent 1.5 (which has infinite variance) has the same Gini index as any exponential distribution (a mere 0.5). This is…
An extension of the latent class model is presented for clustering categorical data by relaxing the classical "class conditional independence assumption" of variables. This model consists in grouping the variables into inter-independent and…
Random binnings generated via recursive binary splits are introduced as a way to detect, measure the strength of, and to display the pattern of association between any two variates, whether one or both are continuous or categorical. This…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
The Gini coefficient is an universally used measurement of income inequality. Intersectoral GDP contributions reveal the economic development of different sectors of the national economy. Linking intersectoral GDP contributions to Gini…
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based…
In this paper, we extend distance correlation to categorical data with general encodings, such as one-hot encoding for nominal variables and semicircle encoding for ordinal variables. Unlike existing methods, our approach leverages the…
This paper proposes a geometric estimator of dependency between a pair of multivariate samples. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate…
This paper introduces a novel methodology for constructing multiclass ROC curves using the multidimensional Gini index. The proposed methodology leverages the established relationship between the Gini coefficient and the ROC Curve and…
Test of 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 numerous…
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions, and applications of distance correlation have been discussed in the recent…
The maximal information coefficient (MIC), which measures the amount of dependence between two variables, is able to detect both linear and non-linear associations. However, computational cost grows rapidly as a function of the dataset…
We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…
We demonstrate how to test for conditional independence of two variables with categorical data using Poisson log-linear models. The size of the conditioning set of variables can vary from 0 (simple independence) up to many variables. We…
Quantifying cooperation or synergy among random variables in predicting a single target random variable is an important problem in many complex systems. We review three prior information-theoretic measures of synergy and introduce a novel…
We propose three measures of mutual dependence between multiple random vectors. All the measures are zero if and only if the random vectors are mutually independent. The first measure generalizes distance covariance from pairwise dependence…
The Gini index is a number that attempts to measure how equitably a resource is distributed throughout a population, and is commonly used in economics as a measurement of inequality of wealth or income. The Gini index is often defined as…
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…
The Gini index signals only the dispersion of the distribution and is not very sensitive to income differences at the tails of the distribution. The widely used index of inequality can be adjusted to also measure distributional asymmetry by…
Understanding epistasis (genetic interaction) may shed some light on the genomic basis of common diseases, including disorders of maximum interest due to their high socioeconomic burden, like schizophrenia. Distance correlation is an…