In this paper, we study the problem of quantitative group testing (QGT) and analyze the performance of three models: the noiseless model, the additive Gaussian noise model, and the noisy Z-channel model. For each model, we analyze two algorithmic approaches: a linear estimator based on correlation scores, and a least squares estimator (LSE). We derive upper bounds on the number of tests required for exact recovery with vanishing error probability, and complement these results with information-theoretic lower bounds. In the additive Gaussian noise setting, our lower and upper bounds match in order.

翻译：本文研究定量群组检测问题，并分析了三种模型的性能：无噪声模型、加性高斯噪声模型以及噪声Z信道模型。针对每种模型，我们分析了两种算法方法：基于相关性分数的线性估计器以及最小二乘估计器。我们推导了在误差概率趋于零的条件下实现精确恢复所需测试次数的上界，并通过信息论下界对这些结果进行了补充。在加性高斯噪声设定中，我们的下界与上界在量级上匹配。