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: efficient algorithms with
practical storage and computation requirements, achievability bounds for
optimal decoding methods, 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" 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.
Description
[1902.06002] Group testing: an information theory perspective
Links and resources
Tags