相关论文: Discovering general multidimensional associations

To quantify the dependence between two random vectors of possibly different dimensions, we propose to rely on the properties of the 2-Wasserstein distance. We first propose two coefficients that are based on the Wasserstein distance between…

Total correlation (TC) is a fundamental concept in information theory that measures statistical dependency among multiple random variables. Recently, TC has shown noticeable effectiveness as a regularizer in many learning tasks, where the…

We suggest novel correlation coefficients which equal the maximum correlation for a class of bivariate Lancaster distributions while being only slightly smaller than maximum correlation for a variety of further bivariate distributions. In…

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 highlight that match fixed effects, represented by the coefficients of interaction terms involving dummy variables for two elements, lack identification without specific restrictions on parameters. Consequently, the coefficients…

Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…

This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…

High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current…

In exploratory data analysis, we are often interested in identifying promising pairwise associations for further analysis while filtering out weaker, less interesting ones. This can be accomplished by computing a measure of dependence on…

The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…

Higher-order information theory has become a rapidly growing toolkit in computational neuroscience, motivated by the idea that multivariate dependencies can reveal aspects of neural computation and communication that are invisible to…

Effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size. Existing effect size indices are developed for particular parametric models or…

Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…

Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…

Measuring the statistical dependence between observed signals is a primary tool for scientific discovery. However, biological systems often exhibit complex non-linear interactions that currently cannot be captured without a priori knowledge…

Our aim is to detect mechanistic interaction between the effects of two causal factors on a binary response, as an aid to identifying situations where the effects are mediated by a common mechanism. We propose a formalization of mechanistic…

Latent variable models are popularly used to measure latent factors (e.g., abilities and personalities) from large-scale assessment data. Beyond understanding these latent factors, the covariate effect on responses controlling for latent…

For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…

We introduce a new information theoretic measure of quantum correlations for multiparticle systems. We use a form of multivariate mutual information -- the interaction information and generalize it to multiparticle quantum systems. There…

A common concern when trying to draw causal inferences from observational data is that the measured covariates are insufficiently rich to account for all sources of confounding. In practice, many of the covariates may only be proxies of the…