Related papers: On combinatorial testing problems
We consider the hypothesis testing problem of deciding whether an observed high-dimensional vector has independent normal components or, alternatively, if it has a small subset of correlated components. The correlated components may have a…
In this paper, a problem of testing is discussed when the samples have been drawn from the normal distribution. The study of hypothesis testing is also extended to Baye's set up.
In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in R^n belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors…
We examine the following version of a classic combinatorial search problem introduced by R\'enyi: Given a finite set $X$ of $n$ elements we want to identify an unknown subset $Y \subset X$ of exactly $d$ elements by testing, by as few as…
We consider the problems of hypothesis testing on a probability measure of independent sample, on solution of ill-posed problem, on deconvolution problem and on Poisson mean measure. For all these setups necessary conditions and sufficient…
This paper studies the problem of discriminating two multivariate Gaussian distributions in a distributed manner. Specifically, it characterizes in a special case the optimal typeII error exponent as a function of the available…
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…
In network tomography, one goal is to identify a small set of failed links in a network, by sending a few packets through the network and seeing which reach their destination. This problem can be seen as a variant of combinatorial group…
We study the following fundamental hypothesis testing problem, which we term Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on $\mathbb{R}^d$, the task is to distinguish, with high probability, between the following…
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. We assume that this set is selected via a very simple approach that is commonly used across scientific disciplines:…
Group testing is a long studied problem in combinatorics: A small set of $r$ ill people should be identified out of the whole ($n$ people) by using only queries (tests) of the form "Does set X contain an ill human?". In this paper we…
We discuss a general approach to handling "multiple hypotheses" testing in the case when a particular hypothesis states that the vector of parameters identifying the distribution of observations belongs to a convex compact set associated…
This paper studies model checking for general parametric regression models having no dimension reduction structures on the predictor vector. Using any U-statistic type test as an initial test, this paper combines the sample-splitting and…
In combinatorial group testing problems Questioner needs to find a defective element $x\in [n]$ by testing subsets of $[n]$. In [18] the authors introduced a new model, where each element knows the answer for those queries that contain it…
Necessary and sufficient conditions of uniform consistency are explored. A hypothesis is simple. Nonparametric sets of alternatives are bounded convex sets in $\mathbb{L}_p$, $p >1$ with "small" balls deleted. The "small" balls have the…
In group testing, simple binary-output tests are designed to identify a small number $t$ of defective items that are present in a large population of $N$ items. Each test takes as input a group of items and produces a binary output…
We consider the task of Gaussian mean testing, that is, of testing whether a high-dimensional vector perturbed by white noise has large magnitude, or is the zero vector. This question, originating from the signal processing community, has…
Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
We consider a compound testing problem within the Gaussian sequence model in which the null and alternative are specified by a pair of closed, convex cones. Such cone testing problem arise in various applications, including detection of…