图感知的局部聚集感染群体检测
Graph-Aware Group Testing with Locally Clustered Infections
- College of Control Science and Engineering, Zhejiang University（浙江大学控制科学与工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出仅依赖接触图的图感知群体检测框架，通过最优传输池化设计、感染集刻画和图全变分解码器，在局部聚集感染下降低测试需求并实现精确恢复。
AI中文摘要：
群体检测被广泛用于以有限数量的测试识别感染者，通常假设感染是独立的。近期研究利用了个体之间的相关性，但往往需要接触图之外的额外信息，如社区结构、交互强度或详细的感染动态。这些信息在实践中可能不可用、不完整或不可靠。在本工作中，我们假设仅已知接触图，并开发了一个图感知的群体检测框架，在池化设计、恢复的基本极限和解码中利用局部化感染聚集。具体而言，我们提出了一种基于最优传输的池化设计，将图邻近性和池化约束纳入统一的优化框架。我们证明，在温和条件下，所提出的设计比伯努利池化设计以更高概率消除未感染个体，从而减少解码的可行搜索空间。然后，我们刻画了由局部化感染聚集引起的可能感染集族，并推导了精确恢复所需测试数量的必要条件，揭示出比组合先验下更低的测试需求。对于解码，我们将人群的感染状态建模为分段常数图信号，并提出一种图全变分正则化解码器。我们在无噪声和有噪声设置下建立了伯努利池化设计下精确恢复的充分条件，并表明在无噪声情况下温和条件下O(Klog(n/K))次测试是充分的。在合成和真实世界网络上的大量模拟证明了所提出框架的有效性，以及在群体检测中利用图诱导相关性的益处。
英文摘要：
Group testing has been widely used to identify infected individuals with a limited number of tests, typically under the assumption of independent infections. Recent studies have exploited correlations among individuals, but often require additional information beyond the contact graph, such as community structures, interaction strengths, or detailed infection dynamics. Such information may be unavailable, incomplete or unreliable in practice. In this work, we assume that only the contact graph is known and develop a graph-aware group testing framework that exploits localized infection clustering in pooling design, fundamental limits of recovery, and decoding. Specifically, we propose an optimal transport-based pooling design that incorporates graph proximity and pooling constraints into a unified optimization framework. We prove that, under mild conditions, the proposed design eliminates uninfected individuals with higher probability than the Bernoulli pooling design, reducing the feasible search space for decoding. Then, we characterize the family of possible infected sets induced by localized infection clustering and derive necessary conditions on the number of tests required for exact recovery, revealing a lower testing requirement than that under the combinatorial prior. For decoding, we model the infection states of the population as a piecewise-constant graph signal and propose a graph total variation regularized decoder. We establish sufficient conditions for exact recovery under the Bernoulli pooling design in both noiseless and noisy settings, and show that O(Klog(n/K)) tests are sufficient under mild conditions in the noiseless case. Extensive simulations on synthetic and real-world networks demonstrate the effectiveness of the proposed framework and the benefit of exploiting graph-induced correlations in group testing.
