Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates
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/\sqrt{n}+\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.
Cite
Text
Wang et al. "Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates." International Conference on Artificial Intelligence and Statistics, 2016.Markdown
[Wang et al. "Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates." International Conference on Artificial Intelligence and Statistics, 2016.](https://mlanthology.org/aistats/2016/wang2016aistats-precision/)BibTeX
@inproceedings{wang2016aistats-precision,
title = {{Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates}},
author = {Wang, Lingxiao and Ren, Xiang and Gu, Quanquan},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2016},
pages = {177-185},
url = {https://mlanthology.org/aistats/2016/wang2016aistats-precision/}
}