Adaptive Group Testing with Mismatched Models

TL;DR

This paper proposes an adaptive Bayesian group testing framework that accounts for test noise and model mismatch, optimizing group selection to efficiently identify infected individuals in low-prevalence scenarios.

Contribution

It introduces a Bayesian optimal experimental design approach for adaptive group testing considering test noise and model mismatch effects.

Findings

Analyzes the impact of test noise and model mismatch on sample complexity.

Develops a utility-based group selection strategy using mutual information.

Provides theoretical insights into the number of tests needed under mismatched models.

Abstract

Accurate detection of infected individuals is one of the critical steps in stopping any pandemic. When the underlying infection rate of the disease is low, testing people in groups, instead of testing each individual in the population, can be more efficient. In this work, we consider noisy adaptive group testing design with specific test sensitivity and specificity that select the optimal group given previous test results based on pre-selected utility function. As in prior studies on group testing, we model this problem as a sequential Bayesian Optimal Experimental Design (BOED) to adaptively design the groups for each test. We analyze the required number of group tests when using the updated posterior on the infection status and the corresponding Mutual Information (MI) as our utility function for selecting new groups. More importantly, we study how the potential bias on the ground-truth noise of group tests may affect the group testing sample complexity.