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

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates %A Lingxiao Wang %A Xiang Ren %A Quanquan Gu %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-wang16a %I PMLR %P 177--185 %U https://proceedings.mlr.press/v51/wang16a.html %V 51 %X 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.
RIS
TY - CPAPER TI - Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates AU - Lingxiao Wang AU - Xiang Ren AU - Quanquan Gu BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-wang16a PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 177 EP - 185 L1 - http://proceedings.mlr.press/v51/wang16a.pdf UR - https://proceedings.mlr.press/v51/wang16a.html AB - 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. ER -
APA
Wang, L., Ren, X. & Gu, Q.. (2016). Precision Matrix Estimation in High Dimensional Gaussian Graphical Models with Faster Rates. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:177-185 Available from https://proceedings.mlr.press/v51/wang16a.html.

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