Ensemble Average Analysis of Non-Adaptive Group Testing with Sparse Pooling Graphs

2025-07-27

AI Summary

This work systematically analyzes the joint behavior of false alarm (FA) and missed detection (MD) probabilities for sparse pooling graph–driven non-adaptive group testing under noiseless, non-quantitative settings. We propose a set-averaged theoretical framework: for ensembles of sparse pooling graphs satisfying a prescribed degree distribution, we derive closed-form expressions for the average FA and MD probabilities under both the Combinatorial Orthogonal Matching Pursuit (COMP) and the Definite Defects Detection (DD) algorithms. Our approach integrates combinatorial modeling with graph-structure averaging, eliminating dependence on individual graph realizations and enabling universal performance characterization. The analysis is mathematically rigorous, and extensive numerical experiments demonstrate excellent agreement with theoretical predictions—validating the accuracy, robustness, and practical utility of the framework for performance evaluation. Moreover, it provides analytically tractable design principles for sparse pooling graphs.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models
• Search and Optimization: Combinatorial Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

A combinatorial analysis of the false alarm (FA) and misdetection (MD) probabilities of non-adaptive group testing with sparse pooling graphs is developed. The analysis targets the combinatorial orthogonal matching pursuit and definite defective detection algorithms in the noiseless, non-quantitative setting. The approach follows an ensemble average perspective, where average FA/MD probabilities are computed for pooling graph ensembles with prescribed degree distributions. The accuracy of the analysis is demonstrated through numerical examples, showing that the proposed technique can be used to characterize the performance of non-adaptive group testing schemes based on sparse pooling graphs.

Problem

• Analyze false alarm and misdetection in non-adaptive group testing
• Evaluate combinatorial algorithms for sparse pooling graphs
• Characterize performance via ensemble average probabilities

Innovation

• Combinatorial analysis of FA and MD probabilities
• Ensemble average perspective for pooling graphs
• Non-adaptive group testing with sparse graphs