The Noisy Quantitative Group Testing Problem

TL;DR

This paper investigates the quantitative group testing problem under various noise models, analyzing algorithmic performance and deriving bounds on the number of tests needed for exact recovery.

Contribution

It provides a comprehensive analysis of QGT under different noise conditions, including bounds and comparisons of linear and least squares estimators.

Findings

Upper bounds on tests for exact recovery derived for each noise model

Lower bounds match upper bounds in the Gaussian noise setting

Performance analysis of correlation-based and least squares estimators

Abstract

In this paper, we study the problem of quantitative group testing (QGT) and analyze the performance of three models: the noiseless model, the additive Gaussian noise model, and the noisy Z-channel model. For each model, we analyze two algorithmic approaches: a linear estimator based on correlation scores, and a least squares estimator (LSE). We derive upper bounds on the number of tests required for exact recovery with vanishing error probability, and complement these results with information-theoretic lower bounds. In the additive Gaussian noise setting, our lower and upper bounds match in order.