Related papers: Small-Error Cascaded Group Testing
In this work we study the fundamental limits of approximate recovery in the context of group testing. One of the most well-known, theoretically optimal, and easy to implement testing procedures is the non-adaptive Bernoulli group testing…
Nowadays, the consequences of failure and downtime of distributed systems have become more and more severe. As an obvious solution, these systems incorporate protection mechanisms to tolerate faults that could cause systems failures and…
Debiased estimation has long been an area of research in the group testing literature. This has led to the development of several estimators with the goal of bias minimization and, recently, an unbiased estimator based on sequential…
We propose a novel infection spread model based on a random connection graph which represents connections between $n$ individuals. Infection spreads via connections between individuals and this results in a probabilistic cluster formation…
Assessing risk of cascading failure in an electrical grid requires identifying many small "defective" subsets of the N elements in a power system, such that the simultaneous failure of all elements in a defective set triggers a large…
We consider the problem of identifying infected individuals in a population of size N. We introduce a group testing approach that uses significantly fewer than N tests when infection prevalence is low. The most common approach to group…
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in disjoint communities: each individual participates in a community, and its infection…
In query learning, the goal is to identify an unknown object while minimizing the number of "yes or no" questions (queries) posed about that object. We consider three extensions of this fundamental problem that are motivated by practical…
We study the problem usually referred to as group testing in the context of COVID-19. Given $n$ samples taken from patients, how should we select mixtures of samples to be tested, so as to maximize information and minimize the number of…
We introduce the notion of groupoidal (weak) test category, which is a small category A such that the groupoid-valued presheaves over A models homotopy types in a "canonical and nice" way. The definition does not require a priori that A is…
We consider the group testing problem, in which one seeks to identify a subset of defective items within a larger set of items based on a number of noisy tests. While matching achievability and converse bounds are known in several cases of…
In this paper, we propose algorithms that leverage a known community structure to make group testing more efficient. We consider a population organized in connected communities: each individual participates in one or more communities, and…
This paper considers the problem of Quantitative Group Testing (QGT). Consider a set of $N$ items among which $K$ items are defective. The QGT problem is to identify (all or a sufficiently large fraction of) the defective items, where the…
Group testing is an efficient method for testing a large population to detect infected individuals. In this paper, we consider an efficient adaptive two stage group testing scheme. Using a straightforward analysis, we characterize the…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
Identification of up to $d$ defective items and up to $h$ inhibitors in a set of $n$ items is the main task of non-adaptive group testing with inhibitors. To efficiently reduce the cost of this Herculean task, a subset of the $n$ items is…
Combinatorial group testing (CGT) is used to identify defective items from a set of items by grouping them together and performing a small number of tests on the groups. Recently, group testing has been used to design efficient COVID-19…
We study the group testing problem where the goal is to identify a set of k infected individuals carrying a rare disease within a population of size n, based on the outcomes of pooled tests which return positive whenever there is at least…
Group testing is one of the fundamental problems in coding theory and combinatorics in which one is to identify a subset of contaminated items from a given ground set. There has been renewed interest in group testing recently due to its…
Given $d$ defective items in a population of $n$ items with $d \ll n$, in threshold group testing without gap, the outcome of a test on a subset of items is positive if the subset has at least $u$ defective items and negative otherwise,…