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Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into…
The extent of parallelization of a loop is largely determined by the dependences between its statements. While dependence free loops are fully parallelizable, those with loop carried dependences are not. Dependence distance is a measure of…
When studying convergence of measures, an important issue is the choice of probability metric. In this review, we provide a summary and some new results concerning bounds among ten important probability metrics/distances that are used by…
This paper introduces a simple measure of a concordance pattern among observed outcomes along a network, i.e., the pattern in which adjacent outcomes tend to be more strongly correlated than non-adjacent outcomes. The graph concordance…
If nonlocality is to be inferred from a violation of Bell's inequality, an important assumption is that the measurement settings are freely chosen by the observers, or alternatively, that they are random and uncorrelated with the…
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…
We propose two model-free, permutation-based tests of independence between a pair of random variables. The tests can be applied to samples from any bivariate distribution: continuous, discrete or mixture of those, with light tails or heavy…
A criterion is proposed for testing hypothesis about the nature of the error variance in the dependent variable in linear model, which separates correctly and incorrectly specified models. In the former only measurement errors determine the…
We present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. Our test detects any kind of dependence between the two time series within an arbitrary maximum lag $L$.…
In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain…
Testing for independence between two random vectors is a fundamental problem in statistics. It is observed from empirical studies that many existing omnibus consistent tests may not work well for some strongly nonmonotonic and nonlinear…
Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…
Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of…
Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…
A well-known problem when learning from user clicks are inherent biases prevalent in the data, such as position or trust bias. Click models are a common method for extracting information from user clicks, such as document relevance in web…
In many statistical modeling frameworks, goodness-of-fit tests are typically administered to the estimated residuals. In the time series setting, whiteness of the residuals is assessed using the sample autocorrelation function. For many…
In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…
You measure the value of a quantity x for a number of systems (cells, molecules, people, chunks of metal, DNA vectors, etc.). You repeat the whole set of measures in different occasions or assays, which you try to design as equal to one…
In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…
Explicit finite-sample statistical guarantees on model performance are an important ingredient in responsible machine learning. Previous work has focused mainly on bounding either the expected loss of a predictor or the probability that an…