Related papers: Discovering general multidimensional associations
Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions…
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…
The proposal of Reshef et al. (2011) is an interesting new approach for discovering non-linear dependencies among pairs of measurements in exploratory data mining. However, it has a potentially serious drawback. The authors laud the fact…
The test of independence is a crucial component of modern data analysis. However, traditional methods often struggle with the complex dependency structures found in high-dimensional data. To overcome this challenge, we introduce a novel…
Understanding the relationships between different properties of data, such as whether a connectome or genome has information about disease status, is becoming increasingly important in modern biological datasets. While existing approaches…
Multivariate correlation analysis plays an important role in various fields such as statistics, economics, and big data analytics. In this paper, we propose a pair of measures, the unsigned correlation coefficient (UCC) and the unsigned…
The paper considers variable selection in linear regression models where the number of covariates is possibly much larger than the number of observations. High dimensionality of the data brings in many complications, such as (possibly…
Distance multivariance is a multivariate dependence measure, which can detect dependencies between an arbitrary number of random vectors each of which can have a distinct dimension. Here we discuss several new aspects, present a concise…
We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
We propose a new Gini correlation to measure dependence between a categorical and numerical variables. Analogous to Pearson $R^2$ in ANOVA model, the Gini correlation is interpreted as the ratio of the between-group variation and the total…
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 Maximal Information Coefficient (MIC) of Reshef et al. (Science, 2011) is a statistic for measuring dependence between variable pairs in large datasets. In this note, we prove that MIC is a consistent estimator of the corresponding…
In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus…
Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…
Multiple correlation is a fundamental concept with broad applications. The classical multiple correlation coefficient is developed to assess how strongly a dependent variable is associated with a linear combination of independent variables.…
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…
How does one find dimensions in multivariate data that are reliably expressed across repetitions? For example, in a brain imaging study one may want to identify combinations of neural signals that are reliably expressed across multiple…
Mutual information (MI) is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density…
A coefficient is introduced that quantifies the extent of separation of a random variable $Y$ relative to a number of variables $\mathbf{X} = (X_1, \dots, X_p)$ by skillfully assessing the sensitivity of the relative effects of the…