Aldridge, M orcid.org/0000-0002-9347-1586, Johnson, O and Scarlett, J (2019) Group testing: An Information Theory Perspective. Foundations and Trends in Communications and Information Theory, 15 (3-4). pp. 196-392. ISSN 1567-2190
Abstract
The group testing problem concerns discovering a small number of defective items within a large population by performing tests on pools of items. A test is positive if the pool contains at least one defective, and negative if it contains no defectives. This is a sparse inference problem with a combinatorial flavour, with applications in medical testing, biology, telecommunications, information technology, data science, and more. In this monograph, we survey recent developments in the group testing problem from an information-theoretic perspective. We cover several related developments: achievability bounds for optimal decoding methods, efficient algorithms with practical storage and computation requirements, and algorithm-independent converse bounds. We assess the theoretical guarantees not only in terms of scaling laws, but also in terms of the constant factors, leading to the notion of the rate and capacity of group testing, indicating the amount of information learned per test. Considering both noiseless and noisy settings, we identify several regimes where existing algorithms are provably optimal or near-optimal, as well as regimes where there remains greater potential for improvement. In addition, we survey results concerning a number of variations on the standard group testing problem, including partial recovery criteria, adaptive algorithms with a limited number of stages, constrained test designs, and sublinear-time algorithms.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 M. Aldridge, O. Johnson and J. Scarlett. This is an author produced version of a paper published in Functions and Trends in Communications and Information Theory. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | cs.IT; cs.IT; cs.DM; math.IT; math.PR; math.ST; stat.TH |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Oct 2019 10:57 |
Last Modified: | 05 Jun 2020 00:38 |
Status: | Published |
Publisher: | Now Publishers |
Identification Number: | 10.1561/0100000099 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:151615 |