An Order-Optimal Adaptive Test Plan for Noisy Group Testing Under Unknown Noise Models

We consider the problem of noisy group testing where the test results are corrupted by noise with an unknown distribution. We propose an adaptive test plan consisting of a hierarchy of biased random walks guided by a local sequential test which together lend adaptivity and agnosticism to the unknown noise model. We show that the proposed test plan is order optimal in both the population size and the error rate.

1. INTRODUCTION

Group testing is a common strategy employed to identify defective items from a given population of items. The idea of group testing, initiated by Robert Dorfman [1], involves performing tests over subsets of the population instead of tests on individual items to reduce the number of required tests. There is now a renewed interest in group testing to expedite testing for COVID-19 [2]. The objective under the group testing strategy is to outline a sequence of subsets to be tested so that all the defective items can be identified using a minimum possible number of tests.