利用梯度下降改进分组测试
Improving Group Testing via Gradient Descent
摘要：
研究了具有不同独立先验的分组测试问题。到目前为止，文献中提出的合并策略采用以下方法：提出手工制作的测试设计以及解码策略，并保证有多少测试足以识别人群中的所有感染。在本文中，我们采取了一种不同的，但也许更实用的方法：我们固定解码器和测试的数量，我们问，鉴于这些，什么是最好的测试设计可以使用？我们探讨这个问题的确定非缺陷（DND）解码器。我们制定一个（非凸）优化问题，其中的目标函数是一个特定的设计的预期错误数。我们通过梯度下降找到近似的解决方案，我们进一步优化知情的初始化。我们通过模拟说明，我们的方法可以实现显着的性能改善传统的方法。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
