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 language||English (US)|
|Title of host publication||26th International Joint Conference on Artificial Intelligence, IJCAI 2017|
|Publisher||International Joint Conferences on Artificial Intelligence|
|Number of pages||7|
|State||Published - 2017|
|Event||26th International Joint Conference on Artificial Intelligence, IJCAI 2017 - Melbourne, Australia|
Duration: Aug 19 2017 → Aug 25 2017
|Name||IJCAI International Joint Conference on Artificial Intelligence|
|Other||26th International Joint Conference on Artificial Intelligence, IJCAI 2017|
|Period||8/19/17 → 8/25/17|
Bibliographical noteFunding Information:
This research was supported in part by NSF grant IIS-1319749.