Year: 2025
Type: article
Abstract: We consider the problem of identifying the defectives from a population of items via anon-adaptive group testingframework with a random pooling-matrix design. We analyze the sufficient number of tests needed forapproximate set identification, i.e., for identifyingalmostall the defective and non-defective items with highconfidence. To this end, we view the group testing problem as a function learning problem in the probably approximately correct (PAC) framework. We derive sufficiency bounds on the number of tests for popular binary group testing recovery algorithms, namely, combinatorial orthogonal matching pursuit under Bernoulli and near-constant row-weight test designs, and definite defectives under a Bernoulli test design. We compare the derived bounds with the existing ones in the literature for exact recovery both theoretically and using simulations. Finally, we contrast the three cases under consideration in terms of the sufficient testing ratesurfaceand the sufficient number of testscontoursacross the range of the approximation and confidence levels.
Authors: Sameera Bharadwaja H., Chandra R. Murthy
Institution: Indian Institute of Science Bangalore
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4408565167