Scheduling Improves the Performance of Belief Propagation for Noisy Group Testing

TL;DR

This paper demonstrates that scheduling belief propagation algorithms significantly enhances the detection accuracy in noisy group testing, especially in practical, limited-item scenarios, by reducing false negatives and positives.

Contribution

It introduces two variants of belief propagation algorithms inspired by coding theory, showing they outperform traditional methods in noisy group testing through extensive simulations.

Findings

Reduced false-negative rate by about 50% under the combinatorial model.

False-negative rate reduction increases to about 80% under the probabilistic model.

Algorithms achieve higher success probability and lower error rates.

Abstract

This paper considers the noisy group testing problem where among a large population of items some are defective. The goal is to identify all defective items by testing groups of items, with the minimum possible number of tests. The focus of this work is on the practical settings with a limited number of items rather than the asymptotic regime. In the current literature, belief propagation has been shown to be effective in recovering defective items from the test results. In this work, we adopt two variants of the belief propagation algorithm for the noisy group testing problem. These algorithms have been used successfully in the decoding of low-density parity-check codes. We perform an experimental study and using extensive simulations we show that these algorithms achieve higher success probability, lower false-negative, and false-positive rates compared to the traditional belief propagation algorithm. For instance, our results show that the proposed algorithms can reduce the false-negative rate by about $50\%$ (or more) when compared to the traditional BP algorithm, under the combinatorial model. Moreover, under the probabilistic model, this reduction in the false-negative rate increases to about $80\%$ for the tested cases.