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Time varying undirected graphs

Zhou, Shuheng ; Lafferty, John ; Wasserman, Larry

In: Machine Learning, 2010, vol. 80, no. 2-3, p. 295-319

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    Titre
    • Time varying undirected graphs
    Auteur
    • Zhou, Shuheng. Seminar für Statistik, ETH Zürich HG G 10.2, Rämistrasse 101, 8092, Zürich, Switzerland
    • Lafferty, John. Computer Science Department, Carnegie Mellon University, 5000 Forbes Ave., 15213, Pittsburgh, PA, USA
    • Wasserman, Larry. Department of Statistics, Carnegie Mellon University, 5000 Forbes Ave., 15213, Pittsburgh, PA, USA
    Type de document
    • Postprint
    Langue
    • Inglese
    Publié dans
    • Machine Learning, 2010, vol. 80, no. 2-3, p. 295-319. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:312720
    Summary
    Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using ℓ 1 penalization methods. However, current methods assume that the data are independent and identically distributed. If the distribution, and hence the graph, evolves over time then the data are not longer identically distributed. In this paper we develop a nonparametric method for estimating time varying graphical structure for multivariate Gaussian distributions using an ℓ 1 regularization method, and show that, as long as the covariances change smoothly over time, we can estimate the covariance matrix well (in predictive risk) even when p is large