StarTrek: Combinatorial variable selection with false discovery rate control
StarTrek：控制错误发现率的组合变量选择AI 解读 ↓
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StarTrek：控制错误发现率的组合变量选择
- 研究问题
- 在高维网络中，如何选择节点度数超过给定阈值的枢纽节点，并在组合结构和复杂检验依赖下控制错误发现率？
- 方法与思路
- 作者提出StarTrek筛选器，以高斯乘子自助法构造最大统计量的p值，并用高维高斯向量的Cramér型比较界分析误差。
- 材料陈述的贡献
- 摘要称，该方法可控制枢纽发现的错误发现率，并可扩展至其他离散结构检验；作者给出数值实验及基因调控应用。
- 阅读关注点
- 应核对图模型假设、度数阈值、最大统计量和p值构造，以及相对比较界、检验依赖与错误发现率控制之间的关系。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明；摘要未列完整控制条件或数值结果，基因网络应用也不直接证明经济网络中的适用性。
原文摘要
Variable selection on the large-scale networks has been extensively studied in the literature. While most of the existing methods are limited to the local functionals especially the graph edges, this paper focuses on selecting the discrete hub structures of the networks. Specifically, we propose an inferential method, called StarTrek filter, to select the hub nodes with degrees larger than a certain thresholding level in the high-dimensional graphical models and control the false discovery rate (FDR). Discovering hub nodes in the networks is challenging: there is no straightforward statistic for testing the degree of a node due to the combinatorial structures; complicated dependence in the multiple testing problem is hard to characterize and control. In methodology, the StarTrek filter overcomes this by constructing p-values based on the maximum test statistics via the Gaussian multiplier bootstrap. In theory, we show that the StarTrek filter can control the FDR by providing accurate bounds on the approximation errors of the quantile estimation and addressing the dependence structures among the maximal statistics. To this end, we establish novel Cramér-type comparison bounds for the high-dimensional Gaussian random vectors. Compared to the Gaussian comparison bound via the Kolmogorov distance established by Chernozhukov, Chetverikov and Kato (Ann. Statist. 42 (2014) 1787–1818), our Cramér-type comparison bounds establish the relative difference between the distribution functions of two high-dimensional Gaussian random vectors, which is essential in the theoretical analysis of FDR control. Moreover, the StarTrek filter can be applied to general statistical models for FDR control of discovering discrete structures such as simultaneously testing the sparsity levels of multiple high-dimensional linear models. We illustrate the validity of the StarTrek filter in a series of numerical experiments and apply it to the genotype-tissue expression dataset to discover central regulator genes.