Noisy Adaptive Group Testing using Bayesian Sequential Experimental Design.

When test resources are scarce, a viable alternative to test for the presence of a pathogen in a population of $n$ patients is to use group tests rather than individual tests. This is sometimes possible by pooling samples (e.g. swabs) from individuals, and test for the presence of the pathogen (e.g. virus RNA) in that pool. We propose a new adaptive and iterative group testing procedure that selects groups to test next, given the outcomes of past noisy tests. We model this problem as a Bayesian sequential experimental design problem. Given previous group test results, a crucial element of our approach lies in sampling the posterior distribution (among all $2^n$ possible states) using sequential Monte Carlo samplers. We then use these samples to estimate and optimize an utility function to select groups. We focus in our experiments on the mutual information of future tests, and use a greedy solver. We also propose a simpler, lightweight method that is only informed by the marginal distribution of the posterior, which can be approximated using loopy belief propagation. We illustrate the performance of our approach using a simulator that can take into account various realistic constraints (noise of tests varying with group size, maximum capacity of tests per cycle, maximum size of pools etc.), and show a significant empirical improvement in detection of infections over more standard group testing procedures.