Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates

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Lingxiao Wang, Xiang Ren, Quanquan Gu ;
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:177-185, 2016.

Abstract

In this paper, we present a new estimator for precision matrix in high dimensional Gaussian graphical models. At the core of the proposed estimator is a collection of node-wise linear regression with nonconvex penalty. In contrast to existing estimators for Gaussian graphical models with O(s\sqrt\log d/n) estimation error bound in terms of spectral norm, where s is the maximum degree of a graph, the proposed estimator could attain O(s/\sqrtn+\sqrt\log d/n) spectral norm based convergence rate in the best case, and it is no worse than exiting estimators in general. In addition, our proposed estimator enjoys the oracle property under a milder condition than existing estimators. We show through extensive experiments on both synthetic and real datasets that our estimator outperforms the state-of-the art estimators.

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