Inverse covariance estimation with structured groups

Shaozhe Tao, Yifan Sun, Daniel L Boley

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Estimating the inverse covariance matrix of p variables from n observations is challenging when np, since the sample covariance matrix is singular and cannot be inverted. A popular solution is to optimize for the l1 penalized estimator; however, this does not incorporate structure domain knowledge and can be expensive to optimize. We consider finding inverse covariance matrices with group structure, defined as potentially overlapping principal submatrices, determined from domain knowledge (e.g. categories or graph cliques). We propose anew estimator for this problem setting that can be derived efficiently via the Frank-Wolfe method, leveraging chordal decomposition theory for scalability. Simulation results show significant improvement in sample complexity when the correct group structure is known. We also apply these estimators to 14,910 stock closing prices, with noticeable improvement when group sparsity is exploited.

Original languageEnglish (US)
Title of host publication26th International Joint Conference on Artificial Intelligence, IJCAI 2017
EditorsCarles Sierra
PublisherInternational Joint Conferences on Artificial Intelligence
Number of pages7
ISBN (Electronic)9780999241103
StatePublished - 2017
Event26th International Joint Conference on Artificial Intelligence, IJCAI 2017 - Melbourne, Australia
Duration: Aug 19 2017Aug 25 2017

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823


Other26th International Joint Conference on Artificial Intelligence, IJCAI 2017

Bibliographical note

Funding Information:
This research was supported in part by NSF grant IIS-1319749.


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