Nonparametric regression with homogeneous group testing data

TL;DR

This paper proposes new nonparametric predictors for homogeneous pooled data in group testing, achieving optimal convergence rates and outperforming existing methods, especially under moderate pooling levels.

Contribution

It introduces novel nonparametric predictors for pooled data that attain optimal convergence rates, improving upon previous random-pooling methods.

Findings

Achieves optimal convergence rates for moderate pooling levels.

Convergence rate under over-pooling differs from optimal by at most a logarithmic factor.

Outperforms existing random-pooling nonparametric predictor.

Abstract

We introduce new nonparametric predictors for homogeneous pooled data in the context of group testing for rare abnormalities and show that they achieve optimal rates of convergence. In particular, when the level of pooling is moderate, then despite the cost savings, the method enjoys the same convergence rate as in the case of no pooling. In the setting of "over-pooling" the convergence rate differs from that of an optimal estimator by no more than a logarithmic factor. Our approach improves on the random-pooling nonparametric predictor, which is currently the only nonparametric method available, unless there is no pooling, in which case the two approaches are identical.