Approximate Set Identification: PAC Analysis for Group Testing

Bharadwaja H, S and Bansal, M and Murthy, CR (2022) Approximate Set Identification: PAC Analysis for Group Testing. In: 2022 IEEE International Symposium on Information Theory, ISIT 2022, 26 June 2022 through 1 July 2022, Espoo, pp. 2237-2242.

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Abstract

In this paper, we derive sufficiency results on the number of group tests required, in a non-adaptive random pooling matrix setting, to find almost all the defective and non-defective items with high confidence, via two popular algorithms in the group testing literature, namely CoMa and DD. To this end, we propose viewing the group testing problem as an online function learning problem and develop our analysis using the probably approximately correct (PAC) framework. We compare the derived bounds with existing bounds literature for exact recovery both theoretically and using simulations. We also illustrate the savings in the number of tests required for approximate defective set recovery compared to exact recovery. © 2022 IEEE.

Item Type:	Conference Paper
Publication:	IEEE International Symposium on Information Theory - Proceedings
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to the IEEE.
Keywords:	Defects; Recovery; Signal reconstruction, Approximate sets; Defective items; Exact recoveries; Group testing; High confidence; matrix; Online learning; Probably approximately correct; Probably approximately correct learning; Sparse signal recoveries, E-learning
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	06 Sep 2022 07:00
Last Modified:	06 Sep 2022 07:00
URI:	https://eprints.iisc.ac.in/id/eprint/76474

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