Related papers: A Novel Multiscale Framework for Testing Independe…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
We consider the following problem: given the weights of two models, can we test whether they were trained independently -- i.e., from independent random initializations? We consider two settings: constrained and unconstrained. In the…
When two variables are related by a known function, the coefficient of determination (denoted $R^2$) measures the proportion of the total variance in the observations that is explained by that function. This quantifies the strength of the…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
In a bivariate setting, we consider the problem of detecting a sparse contamination or mixture component, where the effect manifests itself as a positive dependence between the variables, which are otherwise independent in the main…
Ultrahigh-dimensional variable selection plays an increasingly important role in contemporary scientific discoveries and statistical research. Among others, Fan and Lv [J. R. Stat. Soc. Ser. B Stat. Methodol. 70 (2008) 849-911] propose an…
We show that the stochastic independence of real-valued random variables is equivalent to the conditional uncorrelation, where the conditioning takes place over the Cartesian products of intervals. Next, we express the mutual independence…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
Testing for conditional independence is a core aspect of constraint-based causal discovery. Although commonly used tests are perfect in theory, they often fail to reject independence in practice, especially when conditioning on multiple…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…
Tests of independence are an important tool in applications, specifically in connection with the detection of a relationship between variables; they also have initiated many developments in statistical theory. In the present paper we build…
The problem of signal detection using sparse, faint information is closely related to a variety of contemporary statistical problems, including the control of false-discovery rate, and classification using very high-dimensional data. Each…
Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any…
We propose a simple multivariate normality test based on Kac-Bernstein's characterization, which can be conducted by utilising existing statistical independence tests for sums and differences of data samples. We also perform its empirical…
Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…
Motivated by the importance of measuring the association between the response and predictors in high dimensional data, In this article, we propose a new mean variance test of independence between a categorical random variable and a…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
Relation extraction is the task of identifying predefined relationship between entities, and plays an essential role in information extraction, knowledge base construction, question answering and so on. Most existing relation extractors…
In broad applications, it is routinely of interest to assess whether there is evidence in the data to refute the assumption of conditional independence of $Y$ and $X$ conditionally on $Z$. Such tests are well developed in parametric models…