Efficient pooling designs and screening performance in group testing for two type defectives
Hiroyasu Matsushima, Yusuke Tajima, Xiao-Nan Lu, Masakazu Jimbo
TL;DR
This work extends group testing to two defective types, A and B, by developing a belief propagation (BP) algorithm to compute marginal posteriors from noisy pool results and by constructing pooling designs via finite affine geometry to improve identifiability. The method uses three pool types—testing for A, testing for B, and testing AB (defective if A or B)—and performs BP on corresponding bipartite graphs to infer $\Pr(X_j^A=a, X_j^B=b|s^A,s^B,s^{AB})$. Simulation results show that affine-geometry designs can yield strong screening power (even with multiple defectives per type) whereas short cycles in the pooling graph degrade BP accuracy, underscoring the importance of design structure. Overall, the paper demonstrates that combining BP with carefully constructed pooling designs provides effective, scalable screening for multi-type defectives in noisy group testing and identifies avenues for improving both designs and inference in future work.
Abstract
Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the number of tests. Many research have been developed for group testing for a single type of defectives. In this paper, we consider the case where two types of defective A and B exist. For two types of defectives, we develop a belief propagation algorithm to compute marginal posterior probability of defectives. Furthermore, we construct several kinds of collections of pools in order to test for A and B. And by utilizing our belief propagation algorithm, we evaluate the performance of group testing by conducting simulations.