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Missing values: sparse inverse covariance estimation andanextension to sparse regression

Städler, Nicolas ; Bühlmann, Peter

In: Statistics and Computing, 2012, vol. 22, no. 1, p. 219-235

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    Titre
    • Missing values: sparse inverse covariance estimation andanextension to sparse regression
    Auteur
    • Städler, Nicolas. Seminar für Statistik, ETH Zürich, 8092, Zürich, Switzerland
    • Bühlmann, Peter. Seminar für Statistik, ETH Zürich, 8092, Zürich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Statistics and Computing, 2012, vol. 22, no. 1, p. 219-235. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:320197
    Summary
    We propose an ℓ 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