Estimating Sparse Precision Matrices from Data with Missing Values

• Activity Number: 249
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Mladen Kolar*+ and Eric P. Xing
• Companies: Carnegie Mellon University and Carnegie Mellon University
• Keywords: Convex progam ; EM algorithm ; Gaussian graphical models ; High-dimensional statistics ; Missing data

Abstract

Data sets with missing values arise in many practical problems and domains. However, correct statistical analysis of these data sets is difficult. A popular likelihood approach to statistical inference from partially observed data is the expectation maximization (EM) algorithm, which leads to non-convex optimization and estimates that are difficult to analyze theoretically. We study a simple two step procedure for covariance selection, which is tractable in high-dimensions and does not require imputation of the missing values. We provide rates of convergence for this estimator in the spectral norm, Frobenius norm and element-wise linf norm. Simulation studies show that this estimator compares favorably with the EM algorithm. Our results have important practical consequences as they show that standard tools for covariance selection can be used when data contains missing values, without resorting to the iterative EM algorithm that can be slow to converge in practice for large problems.