Related papers: The Optimality of a Nested Generalized Pairwise Gr…
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…
Ranking and selection (R&S) aims to select the best alternative with the largest mean performance from a finite set of alternatives. Recently, considerable attention has turned towards the large-scale R&S problem which involves a large…
The group testing problem consists of determining a small set of defective items from a larger set of items based on a number of tests, and is relevant in applications such as medical testing, communication protocols, pattern matching, and…
In the group-testing literature, efficient algorithms have been developed to minimize the number of tests required to identify all minimal "defective" sub-groups embedded within a larger group, using deterministic group splitting with a…
We study a hypothesis testing problem in which data is compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and…
The $k$-of-$n$ testing problem involves performing $n$ independent tests sequentially, in order to determine whether/not at least $k$ tests pass. The objective is to minimize the expected cost of testing. This is a fundamental and…
We consider the problem of sequential hypothesis testing by betting. For a general class of composite testing problems -- which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of…
Multiple testing problems are a staple of modern statistical analysis. The fundamental objective of multiple testing procedures is to reject as many false null hypotheses as possible (that is, maximize some notion of power), subject to…
The problem of detecting anomalies in multiple processes is considered. We consider a composite hypothesis case, in which the measurements drawn when observing a process follow a common distribution with an unknown parameter (vector), whose…
The goal of combinatorial group testing is to efficiently identify up to $d$ defective items in a large population of $n$ items, where $d \ll n$. Defective items satisfy certain properties while the remaining items in the population do not.…
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…
Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…
Assuming that data are collected sequentially from independent streams, we consider the simultaneous testing of multiple binary hypotheses under two general setups; when the number of signals (correct alternatives) is known in advance, and…
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…
We study sequential multiple testing with independent data streams, where the goal is to identify an unknown subset of signals while controlling commonly used error metrics, including generalized familywise rates and false discovery and…
In industrial engineering and manufacturing, quality control is an essential part of the production process of a product. To ensure proper functionality of a manufactured good, rigorous testing has to be performed to identify defective…
We study practically efficient methods for performing combinatorial group testing. We present efficient non-adaptive and two-stage combinatorial group testing algorithms, which identify the at most d items out of a given set of n items that…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
Testing of hypotheses is a well studied topic in mathematical statistics. Recently, this issue has also been addressed in the context of Inverse Problems, where the quantity of interest is not directly accessible but only after the…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…