网络多重假设检验的图信号处理视角：控制错误发现率
A Graph Signal Processing Perspective of Network Multiple Hypothesis Testing with False Discovery Rate Control
AI总结：
本文提出一种基于图信号处理的传感器网络多重假设检验方法，通过参数化带限广义图信号估计局部错误发现率，并采用逐步上升程序实现渐近错误发现率控制，数值实验验证其有效性。
摘要：
我们考虑在联合时空域上的传感器网络中的多重假设检验问题。传感器网络被建模为一个图，其中每个顶点代表一个传感器，每个顶点关联一个随时间变化的信号。我们假设在联合时空域的每个样本点都有一个假设检验和相应的$p$-值。我们的目标是确定哪些点具有真实的备择假设。通过将备择假设下未知的$p$-值分布和假设为零的先验概率参数化为带限广义图信号，我们可以获得它们的一致估计。因此，我们也获得了局部错误发现率（lfdr）的估计。我们证明，通过对估计的lfdr使用逐步上升程序，可以在预定水平上实现渐近错误发现率控制。数值实验验证了我们的方法相对于现有方法的有效性。
英文摘要：
We consider a multiple hypothesis testing problem in a sensor network over the joint spatio-temporal domain. The sensor network is modeled as a graph, with each vertex representing a sensor and a signal over time associated with each vertex. We assume a hypothesis test and an associated $p$-value for every sample point in the joint spatio-temporal domain. Our goal is to determine which points have true alternative. By parameterizing the unknown $p$-value distribution under the alternative and the prior probabilities of hypotheses being null with a bandlimited generalized graph signal, we can obtain consistent estimates for them. Consequently, we also obtain an estimate of the local false discovery rates (lfdr). We prove that by using a step-up procedure on the estimated lfdr, we can achieve asymptotic false discovery rate control at a pre-determined level. Numerical experiments validate the effectiveness of our approach compared to existing methods.
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