Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates
Lingxiao Wang, Xiang Ren, Quanquan Gu
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.
BibTeX
@InProceedings{pmlr-v51-wang16a,
title = {Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates},
author = {Wang, Lingxiao and Ren, Xiang and Gu, Quanquan},
booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
pages = {177--185},
year = {2016},
editor = {Gretton, Arthur and Robert, Christian C.},
volume = {51},
series = {Proceedings of Machine Learning Research},
address = {Cadiz, Spain},
month = {09--11 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v51/wang16a.pdf},
url = {https://proceedings.mlr.press/v51/wang16a.html},
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.}
}