Estimating differential latent variable graphical models with applications to brain connectivity

• 成果类型: Article
• 署名作者: Na, S.; Kolar, M.; Koyejo, O.
• 署名单位: University of Chicago; University of Chicago; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa066
• 发表日期: 2021
• 页码: 425442
• 关键词: NETWORKS; Incoherence; matrix; sparsity

摘要

Differential graphical models are designed to represent the difference between the conditional dependence structures of two groups, and thus are of particular interest for scientific investigations. Motivated by modern applications, this manuscript considers an extended setting where each group is generated by a latent variable Gaussian graphical model. Due to the existence of latent factors, the differential network is decomposed into sparse and low-rank components, both of which are symmetric indefinite matrices. We estimate these two components simultaneously using a two-stage procedure: (i) an initialization stage, which computes a simple, consistent estimator, and (ii) a convergence stage, implemented using a projected alternating gradient descent algorithm applied to a nonconvex objective, initialized using the output of the first stage. We prove that given the initialization, the estimator converges linearly with a nontrivial, minimax optimal statistical error. Experiments on synthetic and real data illustrate that the proposed nonconvex procedure outperforms existing methods.