Uniform inference in high-dimensional Gaussian graphical models

• 成果类型: Article
• 署名作者: Klaassen, S.; Kueck, J.; Spindler, M.; Chernozhukov, V
• 署名单位: University of Hamburg; Massachusetts Institute of Technology (MIT)
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac030
• 发表日期: 2023
• 页码: 5168
• 关键词: square-root lasso; confidence-regions; intervals; selection; parameters; bootstrap; tests

摘要

Graphical models have become a popular tool for representing dependencies within large sets of variables and are crucial for representing causal structures. We provide results for uniform inference on high-dimensional graphical models, in which the number of target parameters d is potentially much larger than the sample size, under approximate sparsity. Our results highlight how graphical models can be estimated and recovered using modern machine learning methods in high-dimensional complex settings. To construct simultaneous confidence regions on many target parameters, it is crucial to have sufficiently fast estimation rates of the nuisance functions. In this context, we establish uniform estimation rates and sparsity guarantees for the square-root lasso estimator in a random design under approximate sparsity conditions. These might be of independent interest for related problems in high dimensions. We also demonstrate in a comprehensive simulation study that our procedure has good small sample properties in comparison to existing methods, and we present two empirical applications.