Group testing is a widely used technique for fast testing in medical applications (e.g., blood tests or nasal PCR tests). It has been a particularly popular and powerful strategy during the height of the COVID-19 pandemic when testing resources worldwide were scarce and costly.

Dr. Jonathan Scarlett, a tenure-track assistant professor at the National University of Singapore, has spent years in better understanding the mathematical algorithms and theory behind group testing. Before joining the National University of Singapore, he worked as a postdoctoral fellow at Ecole Polytechnique Fédérale de Lausanne (EPFL) and finished his Ph.D. at the University of Cambridge. His research mainly focused on machine learning, signal processing, and information theory.

In general, the group testing problem consists of determining a small set of defective items (e.g., abstractly representing infected individuals in medical testing) from a larger set of items based on tests on groups of items. It can be thought of as a combinatorial search problem with a flavor of sparse inference. Jonathan’s work provided new precise characterizations of the performance bounds for algorithms and impossibility results, which are the fundamental mathematical limits of the problem.

He has also broadened the scope of the problem by making fundamental contributions on issues such as partial recovery (e.g., tolerating a small number of false positives or false negatives), proving phase transition behavior on how many tests are required, proving achievability and impossibility results on the performance of group testing algorithms under noise, and many other variations on the problem.

According to Jonathan, when it comes to algorithms that tackle group testing problems, they can be adaptive (i.e., each test can be designed depending on past outcomes) or non-adaptive (i.e., all tests must be designed in advance), and can be noiseless (i.e., perfectly reliable outcomes) or noisy (i.e., errors occasionally occur in the test outcomes).

“While optimal noiseless adaptive algorithms have long been known, little attention had been paid to the noisy adaptive setting,” says Jonathan. He focused on this unexplored setting and provided a detailed mathematical understanding of it by developing a practical algorithm with rigorous near-optimality guarantees.

Standard group testing algorithms often have large computational and storage requirements. While these are typically manageable for relatively small problem sizes, they can pose a significant bottleneck in large-scale problems like DNA sequencing. Jonathan proposed notably distinct algorithmic approaches that can address the challenges.

Besides his group testing work, Jonathan adapted his mathematical studies of group testing to other seemingly distinct signal acquisition problems, which are relevant in applications such as magnetic resonance imaging (MRI).

The broad idea in these studies is to seek methods that directly acquire only the “relevant” information during data acquisition. This work led to improved sampling mechanisms for Fourier sampling for MRI, along with a patent.

“Such insights for instance can reduce the time patients stay in an MRI machine, allowing us to diagnose more patients with the same machine. It also allows us to reconstruct images more efficiently, driving down overall costs for the whole imaging pipeline,” says Prof. Volkan Cevher at EPFL.

Jonathan has also contributed to the field of machine learning. His work on Bayesian optimization and bandits has led to publications in machine learning conferences such as NeurIPS, ICML, and COLT.

He is the co-author of several survey articles and monographs, two of which were published by Foundations and Trends in Communications and Information Theory.