张量依赖结构的变更检测：基于稀疏性利用的重排序算法
Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm
AI总结：
针对张量依赖结构变更检测，提出基于稀疏性利用的重排序算法（SERA），通过去相关、中心化及可分离协方差结构增强检验功效，并控制错误发现率，经模拟与科学应用验证有效。
摘要：
张量值数据在广泛的科学应用中频繁出现，其中许多应用可转化为张量依赖结构的变更检测问题。本文在广泛采用的张量正态分布下构建该问题，旨在对张量值观测进行双样本相关/偏相关比较。通过去相关和中心化处理，采用可分离协方差结构来汇集来自不同张量模式（mode）的样本信息，以增强检验的功效。此外，我们提出了一种新颖的稀疏性利用重排序算法（SERA），以进一步提升多重检验的效率。该算法通过结合精心构造的辅助张量序列，对基于主检验统计量得出的p值进行重排序来实现。除了张量框架外，SERA还广泛适用于具有稀疏结构的各类双样本大规模推断问题，具有独立的研究价值。我们推导了所提出检验的渐近性质，并证明该算法能将错误发现率控制在预设水平。通过密集的模拟实验和两项科学应用，我们验证了所提出方法的有效性。
英文摘要：
Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under the popularly adopted tensor-normal distributions and aim at two-sample correlation/partial correlation comparisons of tensor-valued observations. Through decorrelation and centralization, a separable covariance structure is employed to pool sample information from different tensor modes to enhance the power of the test. Additionally, we propose a novel Sparsity-Exploited Reranking Algorithm (SERA) to further improve the multiple testing efficiency. The algorithm is approached through reranking of the p-values derived from the primary test statistics, by incorporating a carefully constructed auxiliary tensor sequence. Besides the tensor framework, SERA is also generally applicable to a wide range of two-sample large-scale inference problems with sparsity structures, and is of independent interest. The asymptotic properties of the proposed test are derived and the algorithm is shown to control the false discovery at the pre-specified level. We demonstrate the efficacy of the proposed method through intensive simulations and two scientific applications.
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。
