Estimating Sparse Precision Matrices from Data with Missing Values

We study a simple two step procedure for estimating sparse precision matrices from data with missing values, 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 ℓ_∞ 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 estimating sparse precision matrices 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.