分组测试的信息论和算法阈值
Information-theoretic and algorithmic thresholds for group testing
摘要：
在群体测试问题中，我们的目标是在一个大的群体中识别出少数受感染的个体。我们利用一个程序，可以测试一组多个人，与测试结果出来积极的，如果至少有一个人在组中被感染。在所有测试同时进行的情况下，确定所有个体的状态所需的最少测试次数是多少？在最近的测试设计中[Aldridge et al. 2016]这些个体被随机分配到测试组，每个个体加入相同数量的组。我们精确地确定了这个随机设计中所需的测试数量的临界值，以便从信息理论上可以推断出每个人的感染状态。此外，我们分析了两个有效的推理算法。这些结果解决了[Aldridge et al.] 2014年，Johnson et al. 2019年]。
英文摘要：
In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff at least one individual in the group is infected. With all tests conducted in parallel, what is the least number of tests required to identify the status of all individuals? In a recent test design [Aldridge et al.\ 2016] the individuals are assigned to test groups randomly, with every individual joining an equal number of groups. We pinpoint the sharp threshold for the number of tests required in this randomised design so that it is information-theoretically possible to infer the infection status of every individual. Moreover, we analyse two efficient inference algorithms. These results settle conjectures from [Aldridge et al.\ 2014, Johnson et al.\ 2019].
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