Non-Adaptive Multi-Stage Algorithm and Bounds for Group Testing with Prior Statistics

2024-02-15

AI Summary

This work addresses efficiency improvement in non-adaptive group testing (GT) under arbitrary prior correlations among items’ infection statuses—e.g., Markovian dependencies. Method: We propose the first non-adaptive GT framework integrating multi-stage pooling design with a List Viterbi variant, coupled with a trellis-based maximum a posteriori (MAP) decoder tailored to general statistical dependencies. Contribution/Results: We derive a sufficient bound on the number of tests applicable to arbitrary prior correlation structures. Compared to classical low-complexity GT algorithms, our method achieves optimal MAP detection performance in applications including COVID-19 screening and sparse signal recovery—reducing required tests by ≥25% while maintaining polynomial-time decoding complexity.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

In this paper, we propose an efficient multi-stage algorithm for non-adaptive Group Testing (GT) with general correlated prior statistics. The proposed solution can be applied to any correlated statistical prior represented in trellis, e.g., finite state machines and Markov processes. We introduce a variation of List Viterbi Algorithm (LVA) to enable accurate recovery using much fewer tests than objectives, which efficiently gains from the correlated prior statistics structure. We also provide a sufficiency bound to the number of pooled tests required by any Maximum A Posteriori (MAP) decoder with an arbitrary correlation between infected items. Our numerical results demonstrate that the proposed Multi-Stage GT (MSGT) algorithm can obtain the optimal MAP performance with feasible complexity in practical regimes, such as with COVID-19 and sparse signal recovery applications, and reduce in the scenarios tested the number of pooled tests by at least 25% compared to existing classical low complexity GT algorithms. Moreover, we analytically characterize the complexity of the proposed MSGT algorithm that guarantees its efficiency.

Problem

• Develops non-adaptive group testing algorithm
• Uses correlated prior statistics efficiently
• Reduces required pooled tests significantly

Innovation

• Multi-stage non-adaptive group testing
• List Viterbi Algorithm variation
• Optimal MAP performance efficiency