Inverse covariance estimation from data with missing values using the Concave-Convex Procedure

We study the problem of estimating sparse precision matrices from data with missing values. We show that the corresponding maximum likelihood problem is a Difference of Convex (DC) program by proving some new concavity results on the Schur complements. We propose a new algorithm to solve this problem based on the ConCave-Convex Procedure (CCCP), and we show that the standard EM procedure is a weaker CCCP for this problem. Numerical experiments show that our new algorithm, called m-CCCP, converges much faster than EM on both synthetic and biology datasets.