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

41 Pages Posted: 31 Aug 2021 Last revised: 7 Oct 2021

See all articles by Kyra Gan

## Kyra Gan

Carnegie Mellon University

## Su Jia

Carnegie Mellon University - David A. Tepper School of Business

## Andrew Li

Carnegie Mellon University

## Sridhar R. Tayur

Carnegie Mellon University - David A. Tepper School of Business

Date Written: July 27, 2021

### Abstract

This paper addresses a set of active learning 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 among a known set of hypotheses. The learner is given a set of actions and knows the random distribution of the outcome of any action under any true hypothesis. Given a target error $\delta>0$, the goal is to sequentially select the fewest number of actions so as to identify the true hypothesis with probability at least $1 - \delta$. Motivated by applications in which the number of hypotheses or actions is massive (e.g., genomics-based cancer detection), we propose efficient (greedy, in fact) 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 outperform previously proposed heuristic policies by large margins.

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

Suggested Citation

Gan, Kyra and Jia, Su and Li, Andrew and Tayur, Sridhar R., Toward a Liquid Biopsy: Greedy Approximation Algorithms for Active Sequential Hypothesis Testing (July 27, 2021). Available at SSRN: https://ssrn.com/abstract=3894600 or http://dx.doi.org/10.2139/ssrn.3894600