Missing values: sparse inverse covariance estimation and an extension to sparse regression

Details Missing values: sparse inverse covariance estimation and an extension to sparse regression Missing values: sparse inverse covariance estimation and an extension to sparse regression

2009-03-31

arxiv.org/abs/0903.5463v3

Statistics and Computing, 2012, Volume 22, 219-235

Statistics

Methodology

The final publication is available at http://www.springerlink.com

Scientific paper

10.1007/s11222-010-9219-7

We propose an l1-regularized likelihood method for estimating the inverse covariance matrix in the high-dimensional multivariate normal model in presence of missing data. Our method is based on the assumption that the data are missing at random (MAR) which entails also the completely missing at random case. The implementation of the method is non-trivial as the observed negative log-likelihood generally is a complicated and non-convex function. We propose an efficient EM algorithm for optimization with provable numerical convergence properties. Furthermore, we extend the methodology to handle missing values in a sparse regression context. We demonstrate both methods on simulated and real data.

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