Toward a Liquid Biopsy: Greedy Approximation Algorithms for Active Sequential Hypothesis Testing

Abstract

This paper addresses a set of problems that occur in the development of liquid biopsies via the lens of active sequential hypothesis testing (ASHT). In the problem of ASHT, a learner seeks to identify the true hypothesis from a known set of hypotheses. The learner is given a set of actions and knows the distribution of the random outcome of any action under any true hypothesis. Given a target error δ > 0, the goal is to sequentially select the fewest number of actions to identify the true hypothesis with probability at least 1-δ. Motivated by applications in which the number of hypotheses or actions is massive (e.g., genomics-based cancer detection), we propose efficient greedy algorithms and provide the first approximation guarantees for ASHT, under two types of adaptivity. Both of our guarantees are independent of the number of actions and logarithmic in the number of hypotheses. We numerically evaluate the performance of our algorithms using both synthetic and real-world DNA mutation data, demonstrating that our algorithms substantially outperform previously proposed heuristic policies.

Keywords: Active Learning, Sequential Hypothesis Testing, Approximation Algorithms, Cancer Detection