相关论文: How to quantify direct correlations between variab…

We compare measures of concordance that arise as Pearson's linear correlation coefficient between two random variables transformed so that they follow the so-called concordance-inducing distributions. The class of such transformed rank…

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…

Predictions are often probabilities; e.g., a prediction could be for precipitation tomorrow, but with only a 30% chance. Given such probabilistic predictions together with the actual outcomes, "reliability diagrams" help detect and diagnose…

Methods to find correlation among variables are of interest to many disciplines, including statistics, machine learning, (big) data mining and neurosciences. Parameters that measure correlation between two variables are of limited utility…

The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from…

We consider the problem of defining the significance of an itemset. We say that the itemset is significant if we are surprised by its frequency when compared to the frequencies of its sub-itemsets. In other words, we estimate the frequency…

Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…

Measuring dependence between two events, or equivalently between two binary random variables, amounts to expressing the dependence structure inherent in a $2\times 2$ contingency table in a real number between $-1$ and $1$. Countless such…

This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and…

This paper proposes two linear projection methods for supervised dimension reduction using only the first and second-order statistics. The methods, each catering to a different parameter regime, are derived under the general Gaussian model…

Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…

We study the value distribution of diagonal forms in k variables and degree d with random real coefficients and positive integer variables, normalized so that mean spacing is one. We show that the l-correlation of almost all such forms is…

Two families of dependence measures between random variables are introduced. They are based on the R\'enyi divergence of order $\alpha$ and the relative $\alpha$-entropy, respectively, and both dependence measures reduce to Shannon's mutual…

An initial screening experiment may lead to ambiguous conclusions regarding the factors which are active in explaining the variation of an outcome variable: thus adding follow-up runs becomes necessary. We propose a fully Bayes objective…

The predictions of text classifiers are often driven by spurious correlations -- e.g., the term `Spielberg' correlates with positively reviewed movies, even though the term itself does not semantically convey a positive sentiment. In this…

Jensen-Shannon divergence is a well known multi-purpose measure of dissimilarity between probability distributions. It has been proven that the square root of this quantity is a true metric in the sense that, in addition to the basic…

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…

Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…

We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…

We consider learning with possibilistic supervision for multi-class classification. For each training instance, the supervision is a normalized possibility distribution that expresses graded plausibility over the classes. From this…