A Probably Approximately Correct Analysis of Group Testing Algorithms

TL;DR

This paper analyzes the number of tests needed in non-adaptive group testing to approximately identify defectives with high confidence, using a PAC framework and comparing three algorithms.

Contribution

It introduces a PAC-based analysis for approximate group testing, deriving bounds for three algorithms and comparing their efficiency and performance.

Findings

Derived sufficiency bounds for test numbers in approximate identification

Compared algorithms in terms of testing rate and confidence levels

Validated bounds through theoretical analysis and simulations

Abstract

We consider the problem of identifying the defectives from a population of items via a non-adaptive group testing framework with a random pooling-matrix design. We analyze the sufficient number of tests needed for approximate set identification, i.e., for identifying almost all the defective and non-defective items with high confidence. To this end, we view the group testing problem as a function learning problem and develop our analysis using the probably approximately correct (PAC) framework. Using this formulation, we derive sufficiency bounds on the number of tests for three popular binary group testing algorithms: column matching, combinatorial basis pursuit, and definite defectives. We compare the derived bounds with the existing ones in the literature for exact recovery theoretically and using simulations. Finally, we contrast the three group testing algorithms under consideration in terms of the sufficient testing rate surface and the sufficient number of tests contours across the range of the approximation and confidence levels.