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

Authors:
Nicolas Städler;Peter Bühlmann
Affiliations:
Seminar für Statistik, ETH Zürich, Zürich, Switzerland 8092;Seminar für Statistik, ETH Zürich, Zürich, Switzerland 8092
Venue:
Statistics and Computing
Year:
2012

Citing 3
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Abstract

We propose an 驴 1-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.