We study the problem of group testing with non-identical, independent priors. So far, the pooling strategies that have been proposed in the literature take the following approach: a hand-crafted test design along with a decoding strategy is proposed, and guarantees are provided on how many tests are sufficient in order to identify all infections in a population. In this paper, we take a different, yet perhaps more practical, approach: we fix the decoder and the number of tests, and we ask, given these, what is the best test design one could use? We explore this question for the Definite Non-Defectives (DND) decoder. We formulate a (non-convex) optimization problem, where the objective function is the expected number of errors for a particular design. We find approximate solutions via gradient descent, which we further optimize with informed initialization. We illustrate through simulations that our method can achieve significant performance improvement over traditional approaches.
翻译:我们用与众不同的独立前科研究群体测试问题。 到目前为止,文献中提议的集合战略采取了以下方法:提出手工制作的测试设计和解码战略,保证有多少测试足以确定人口中的所有感染病例。在本文中,我们采取了不同但也许更实际的方法:我们用非同质、独立的前科来修正解码器和测试数量,我们问,鉴于这些,什么是最佳的测试设计?我们探讨这个问题是为了“不失能(DND)解码器 ” 。我们提出一个(非convex)优化问题,其中目标功能是特定设计的预期误差数。我们通过梯度下降找到近似的解决办法,我们通过知情初始化进一步优化这些解决办法。我们通过模拟来说明我们的方法能够大大改进传统方法的性能。