Time varying undirected graphs

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, evol...

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Bibliographic Details
Published inMachine learning Vol. 80; no. 2-3; pp. 295 - 319
Main Authors Zhou, Shuheng, Lafferty, John, Wasserman, Larry
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.09.2010
Springer Nature B.V
Subjects
Artificial Intelligence
Computer Science
Control
Covariance matrix
Estimates
Estimating
Estimating techniques
Graph theory
Graphs
Machine learning
Mathematics
Mechatronics
Natural Language Processing (NLP)
Normal distribution
Regularization
Risk
Robotics
Simulation and Modeling
Time
Risk consistency
Graph selection
regularization
High dimensional asymptotics
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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.
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ISSN:0885-6125
1573-0565
DOI:10.1007/s10994-010-5180-0