Related papers: Measuring Dependence between Events
Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: $X$ and $Y$. Often, we are interested in understanding how the dependence between $X$ and $Y$ in one set…
Measuring the (causal) direction and strength of dependence between two variables (events), Xi and Xj , is fundamental for all science. Our survey of decades-long literature on statistical dependence reveals that most assume symmetry in the…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
Independence and Conditional Independence (CI) are two fundamental concepts in probability and statistics, which can be applied to solve many central problems of statistical inference. There are many existing independence and CI measures…
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…
A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the…
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…
We propose a coefficient of conditional dependence between two random variables $Y$ and $Z$ given a set of other variables $X_1,\ldots,X_p$, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most…
Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
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…
Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
In this paper, a robust non-parametric measure of statistical dependence, or correlation, between two random variables is presented. The proposed coefficient is a permutation-like statistic that quantifies how much the observed sample S_n :…
For two independent, almost surely finite random variables, independence of their minimum (time) and the event that one of them is either greater, equal or less than the other (cause) is completely characterized. It is shown that, other…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
We discuss the construction of component importance measures for binary coherent reliability systems from known stochastic dependence measures by measuring the dependence between system and component failures. We treat both the…