Related papers: Measuring Dependence between Events
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
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…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
A Bell test can rule out local realistic models, and has potential applications in communications and information tasks. For example, a Bell inequality violation can certify the presence of intrinsic randomness in measurement outcomes,…
Measuring dependence between two random variables is very important, and critical in many applied areas such as variable selection, brain network analysis. However, we do not know what kind of functional relationship is between two…
In this paper we propose several variants to perform the independence test between two random elements based on recurrence rates. We will show how to calculate the test statistic in each one of these cases. From simulations we obtain that…
We conduct a review to assess how the simulation of repeated or recurrent events are planned. For such multivariate time-to-events, it is well established that the underlying mechanism is likely to be complex and to involve in particular…
(To appear in The American Statistician.) Distance covariance (Sz\'ekely, Rizzo, and Bakirov, 2007) is a fascinating recent notion, which is popular as a test for dependence of any type between random variables $X$ and $Y$. This approach…
We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…
We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence…
A popular measure of association is the tail dependence coefficient which measures the strength of dependence in either the lower-left or upper-right tail of a bivariate distribution. In this paper, we develop the idea of quantile…
This paper clarifies a fundamental difference between causal inference and traditional statistical inference by formalizing a mathematical distinction between their respective parameters. We connect two major approaches to causal inference,…
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…
Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…
We propose and axiomatize preferences on a product state space in light of uncertainty regarding the dependency of different payoff-relevant factors. Dependence structures allow to decompose probabilities and allow to pin down behavior…
Given a set of people and a set of events they attend, we address the problem of measuring connectedness or tie strength between each pair of persons given that attendance at mutual events gives an implicit social network between people. We…
Reliability sensitivity analysis is concerned with measuring the influence of a system's uncertain input parameters on its probability of failure. Statistically dependent inputs present a challenge in both computing and interpreting these…
As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…
Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…