Near-Optimal Stochastic Threshold Group Testing

Abstract: We formulate and analyze a stochastic threshold group testing problem motivated by biological applications. Here a set of $n$ items contains a subset of $d \ll n$ defective items. Subsets (pools) of the $n$ items are tested -- the test outcomes are negative, positive, or stochastic (negative or positive with certain probabilities that might depend on the number of defectives being tested in the pool), depending on whether the number of defective items in the pool being tested are fewer than the {\it lower threshold} $l$, greater than the {\it upper threshold} $u$, or in between. The goal of a {\it stochastic threshold group testing} scheme is to identify the set of $d$ defective items via a "small" number of such tests. In the regime that $l = o(d)$ we present schemes that are computationally feasible to design and implement, and require near-optimal number of tests (significantly improving on existing schemes). Our schemes are robust to a variety of models for probabilistic threshold group testing.