Thresholded graphical lasso adjusts for latent variables

• 成果类型: Article
• 署名作者: Wang, Minjie; Allen, Genevera, I
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; Rice University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asac060
• 发表日期: 2023
• 页码: 681697
• 关键词: model selection; COVARIANCE ESTIMATION; likelihood-estimation

摘要

Structural learning of Gaussian graphical models in the presence of latent variables has long been a challenging problem. Chandrasekaran et al. (2012) proposed a convex program for estimating a sparse graph plus a low-rank term that adjusts for latent variables; however, this approach poses challenges from both computational and statistical perspectives. We propose an alternative, simple solution: apply a hard-thresholding operator to existing graph selection methods. Conceptually simple and computationally attractive, the approach of thresholding the graphical lasso is shown to be graph selection consistent in the presence of latent variables under a simpler minimum edge strength condition and at an improved statistical rate. The results are extended to estimators for thresholded neighbourhood selection and constrained L1-minimization for inverse matrix estimation as well. We show that our simple thresholded graph estimators yield stronger empirical results than existing methods for the latent variable graphical model problem, and we apply them to a neuroscience case study on estimating functional neural connections.