Replicates in high dimensions, with applications to latent variable graphical models
本文强调在高维设置中为每个受试者收集多个复制品的重要性，提出一种成对去相关得分检验来推断潜变量图模型的结构，并在脑成像数据上验证了方法的有效性。
In classical statistics, much thought has been put into experimental design and data collection. In the high-dimensional setting, however, experimental design has been less of a focus. In this paper, we stress the importance of collecting multiple replicates for each subject in this setting. We consider learning the structure of a graphical model with latent variables, under the assumption that these variables take a constant value across replicates within each subject. By collecting multiple replicates for each subject, we are able to estimate the conditional dependence relationships among the observed variables given the latent variables. To test the null hypothesis of conditional independence between two observed variables, we propose a pairwise decorrelated score test. Theoretical guarantees are established for parameter estimation and for this test. We show that our proposal is able to estimate latent variable graphical models more accurately than some existing proposals, and apply the proposed method to a brain imaging dataset.