Model-Based and Graph-Based Priors for Group Testing
Ivan Lau, Jonathan Scarlett, and Yang Sun

TL;DR
This paper explores how incorporating structural priors, including subset-based and Ising model-based dependencies, can reduce the number of tests needed for effective group testing, introducing new decoding methods and theoretical insights.
Contribution
It introduces a novel Ising model-based prior for group testing and develops corresponding decoding algorithms, advancing the understanding of prior-informed testing strategies.
Findings
Reduced number of tests with structural priors
Integer Quadratic Program decoder performs well empirically
Theoretical limits are affected by prior assumptions
Abstract
The goal of the group testing problem is to identify a set of defective items within a larger set of items, using suitably-designed tests whose outcomes indicate whether any defective item is present. In this paper, we study how the number of tests can be significantly decreased by leveraging the structural dependencies between the items, i.e., by incorporating prior information. To do so, we pursue two different perspectives: (i) As a generalization of the uniform combinatorial prior, we consider the case that the defective set is uniform over a \emph{subset} of all possible sets of a given size, and study how this impacts the information-theoretic limits on the number of tests for approximate recovery; (ii) As a generalization of the i.i.d.~prior, we introduce a new class of priors based on the Ising model, where the associated graph represents interactions between items. We show that…
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Taxonomy
TopicsSARS-CoV-2 detection and testing · Advanced biosensing and bioanalysis techniques · Biosensors and Analytical Detection
