Group Testing With Side Information via Generalized Approximate Message Passing

Shu-Jie Cao, Ritesh Goenka, Chau-Wai Wong, Ajit Rajwade, Dror Baron

Abstract: Group testing can help maintain a widespread testing program using fewer resources amid a pandemic. In a group testing setup, we are given <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> samples, one per individual. Each individual is either infected or uninfected. These samples are arranged into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m &lt; n$</tex-math></inline-formula> pooled samples, where each pool is obtained by mixing a subset of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> individual samples. Infected individuals are then identified using a group testing algorithm. In this article, we incorporate side information (SI) collected from contact tracing (CT) into nonadaptive/single-stage group testing algorithms. We generate different types of CT SI data by incorporating different possible characteristics of the spread of disease. These data are fed into a group testing framework based on generalized approximate message passing (GAMP). Numerical results show that our GAMP-based algorithms provide improved accuracy.