Precision matrix estimation in high dimensional gaussian graphical models with faster rates

Jianqing Fan Xiang Ren Quanquan Gu

Statistics Theory and Methods mathscidoc:1912.43381

177-185, 2016.5
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 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/ n+ 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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@inproceedings{jianqing2016precision,
  title={Precision matrix estimation in high dimensional gaussian graphical models with faster rates},
  author={Jianqing Fan, Xiang Ren, and Quanquan Gu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114049058524941},
  pages={177-185},
  year={2016},
}
Jianqing Fan, Xiang Ren, and Quanquan Gu. Precision matrix estimation in high dimensional gaussian graphical models with faster rates. 2016. pp.177-185. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114049058524941.
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