Related papers: Detection of Correlated Random Vectors
Chatterjee's rank correlation coefficient $\xi_n$ is an empirical index for detecting functional dependencies between two variables $X$ and $Y$. It is an estimator for a theoretical quantity $\xi$ that is zero for independence and one if…
We propose a method to distinguish causal influence from hidden confounding in the following scenario: given a target variable Y, potential causal drivers X, and a large number of background features, we propose a novel criterion for…
A possible drawback of the ordinary correlation coefficient $\rho$ for two real random variables $X$ and $Y$ is that zero correlation does not imply independence. In this paper we introduce a new correlation coefficient $\rho^*$ which…
In this paper, we propose a novel Euclidean-distance-based coefficient, named differential distance correlation, to measure the strength of dependence between a random variable $ Y \in \mathbb{R} $ and a random vector $ \boldsymbol{X} \in…
There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more…
The identification of the dependent components in multiple data sets is a fundamental problem in many practical applications. The challenge in these applications is that often the data sets are high-dimensional with few observations or…
Testing the independence between random vectors is a fundamental problem in statistics. Distance correlation, a recently popular dependence measure, is universally consistent for testing independence against all distributions with finite…
Measuring strength or degree of statistical dependence between two random variables is a common problem in many domains. Pearson's correlation coefficient $\rho$ is an accurate measure of linear dependence. We show that $\rho$ is a…
A sequential test is proposed for detection and isolation of hubs in a correlation graph. Hubs in a correlation graph of a random vector are variables (nodes) that have a strong correlation edge. It is assumed that the random vectors are…
Testing for dependence has been a well-established component of spatial statistical analyses for decades. In particular, several popular test statistics have desirable properties for testing for the presence of spatial autocorrelation in…
In this paper, we study the problem of determining $k$ anomalous random variables that have different probability distributions from the rest $(n-k)$ random variables. Instead of sampling each individual random variable separately as in the…
This paper investigates the effect of quantization on the performance of the Neyman-Pearson test. It is assumed that a sensing unit observes samples of a correlated stationary ergodic multivariate process. Each sample is passed through an…
The maximal (or Hilbertian) correlation coefficient between two random variables X and Y, denoted by \{X:Y\}, is the supremum of the |Corr(f(X),g(Y))| for real measurable functions f, g, where "Corr" denotes Pearson's correlation…
Group testing, a problem with diverse applications across multiple disciplines, traditionally assumes independence across nodes' states. Recent research, however, focuses on real-world scenarios that often involve correlations among nodes,…
For two correlated graphs which are independently sub-sampled from a common Erd\H{o}s-R\'enyi graph $\mathbf{G}(n, p)$, we wish to recover their \emph{latent} vertex matching from the observation of these two graphs \emph{without labels}.…
In many application domains, networks are observed with node-level features. In such settings, a common problem is to assess whether or not nodal covariates are correlated with the network structure itself. Here, we present four novel…
The growing prevalence of large language models (LLMs) and vision-language models (VLMs) has heightened the need for reliable techniques to determine whether a model has been fine-tuned from or is even identical to another. Existing…
In this article, we study the test for independence of two random elements $X$ and $Y$ lying in an infinite dimensional space ${\cal{H}}$ (specifically, a real separable Hilbert space equipped with the inner product $\langle .,…
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.…
It is frequently of interest to jointly analyze two paired sequences of multiple tests. This paper studies the problem of detecting whether there are more pairs of tests that are significant in both sequences than would be expected by…