Related papers: Detection of Correlated Random Vectors
Consider two sequences of $n$ independent and identically distributed fair coin tosses, $X=(X_1,\ldots,X_n)$ and $Y=(Y_1,\ldots,Y_n)$, which are $\rho$-correlated for each $j$, i.e. $\mathbb{P}[X_j=Y_j] = {1+\rho\over 2}$. We study the…
We consider a distributed source coding problem of $L$ correlated Gaussian observations $Y_i, i=1,2,...,L$. We assume that the random vector $Y^{L}={}^{\rm t} (Y_1,Y_2,$ $...,Y_L)$ is an observation of the Gaussian random vector…
We provide a novel criterion for identifying quantum correlation, which allows us to find connections between Bell type inequalities, entanglement detection, and correlation. We utilize the criterion to construct witness operators that can…
Consider finite sequences $X_{[1,n]}=X_1\dots X_n$ and $Y_{[1,n]}=Y_1\dots Y_n$ of length $n$, consisting of i.i.d.\ samples of random letters from a finite alphabet, and let $S$ and $T$ be chosen i.i.d.\ randomly from the unit ball in the…
Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…
Identifying differences in networks has become a canonical problem in many biological applications. Here, we focus on testing whether two Gaussian graphical models are the same. Existing methods try to accomplish this goal by either…
We study the problem of testing the existence of a heterogeneous dense subhypergraph. The null hypothesis corresponds to a heterogeneous Erd\"{o}s-R\'{e}nyi uniform random hypergraph and the alternative hypothesis corresponds to a…
We propose a new omnibus test for vector white noise using the maximum absolute auto-correlations and cross-correlations of the component series. Based on the newly established approximation by the $L_\infty$-norm of a normal random vector,…
A nonparametric anomalous hypothesis testing problem is investigated, in which there are totally n sequences with s anomalous sequences to be detected. Each typical sequence contains m independent and identically distributed (i.i.d.)…
When testing for the mean vector in a high dimensional setting, it is generally assumed that the observations are independently and identically distributed. However if the data are dependent, the existing test procedures fail to preserve…
Given two networks of differing sizes, it is of interest to test whether the two networks belong to the same distribution. We formalize the notion of "equality of distribution" under the framework of the generalized random dot product…
In variable selection, most existing screening methods focus on marginal effects and ignore dependence between covariates. To improve the performance of selection, we incorporate pairwise effects in covariates for screening and…
Score-based statistical models play an important role in modern machine learning, statistics, and signal processing. For hypothesis testing, a score-based hypothesis test is proposed in \cite{wu2022score}. We analyze the performance of this…
We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
Supporting sampling in the presence of joins is an important problem in data analysis, but is inherently challenging due to the need to avoid correlation between output tuples. Current solutions provide either correlated or non-correlated…
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We…
In this research, inferential theory for hypothesis testing under general convex cone alternatives for correlated data is developed. While there exists extensive theory for hypothesis testing under smooth cone alternatives with independent…
Entries of datasets are often collected only if an event occurred: taking a survey, enrolling in an experiment and so forth. However, such partial samples bias classical correlation estimators. Here we show how to correct for such sampling…
We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized…