We consider the problem of identifying the defectives from a population of items via a non-adaptive group testing framework with a random pooling-matrix design. We analyze the sufficient number of tests needed for approximate set identification, i.e., for identifying almost all the defective and non-defective items with high confidence. To this end, we view the group testing problem as a function learning problem and develop our analysis using the probably approximately correct (PAC) framework. Using this formulation, we derive sufficiency bounds on the number of tests for three popular binary group testing algorithms: column matching, combinatorial basis pursuit, and definite defectives. We compare the derived bounds with the existing ones in the literature for exact recovery theoretically and using simulations. Finally, we contrast the three group testing algorithms under consideration in terms of the sufficient testing rate surface and the sufficient number of tests contours across the range of the approximation and confidence levels.

翻译：本文研究在随机池化矩阵设计的非自适应群体测试框架下，从物品总体中识别缺陷品的问题。我们分析了近似集合识别所需的充分测试次数，即在高置信度下识别几乎所有缺陷品与非缺陷品所需的条件。为此，我们将群体测试问题视为函数学习问题，并基于概率近似正确（PAC）框架展开分析。通过该形式化方法，我们推导了三种主流二元群体测试算法所需测试次数的充分性界：列匹配算法、组合基追踪算法及确定缺陷品算法。我们将所得理论界与文献中现有精确恢复的界进行了理论比较与仿真验证。最后，我们从近似度与置信度参数范围内的充分测试率曲面和充分测试次数等值线两个维度，对比了所研究的三种群体测试算法的性能。