Doubly functional graphical models in high dimensions

• 成果类型: Article
• 署名作者: Qiao, Xinghao; Qian, Cheng; James, Gareth M.; Guo, Shaojun
• 署名单位: University of London; London School Economics & Political Science; University of Southern California; Renmin University of China
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz072
• 发表日期: 2020
• 页码: 415431
• 关键词: inverse covariance estimation; brain activity; selection

摘要

We consider estimating a functional graphical model from multivariate functional observations. In functional data analysis, the classical assumption is that each function has been measured over a densely sampled grid. However, in practice the functions have often been observed, with measurement error, at a relatively small number of points. We propose a class of doubly functional graphical models to capture the evolving conditional dependence relationship among a large number of sparsely or densely sampled functions. Our approach first implements a nonparametric smoother to perform functional principal components analysis for each curve, then estimates a functional covariance matrix and finally computes sparse precision matrices, which in turn provide the doubly functional graphical model. We derive some novel concentration bounds, uniform convergence rates and model selection properties of our estimator for both sparsely and densely sampled functional data in the high-dimensional large-p, small-n regime. We demonstrate via simulations that the proposed method significantly outperforms possible competitors. Our proposed method is applied to a brain imaging dataset.