Graphical nonconvex optimization via an adaptive convex relaxation

Qiang Sun, Kean Ming Tan, Han Liu, Tong Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimation in Gaussian graphical models, which is then approximated by a sequence of adaptive convex programs. Our proposal is computationally tractable and produces an estimator that achieves the oracle rate of convergence. The statistical error introduced by the sequential approximation is clearly demonstrated via a contraction property. The proposed methodology is then extended to modeling semiparametric graphical models. We show via numerical studies that the proposed estimator outperforms other popular methods for estimating Gaussian graphical models.

Original languageEnglish (US)
Title of host publication35th International Conference on Machine Learning, ICML 2018
EditorsAndreas Krause, Jennifer Dy
PublisherInternational Machine Learning Society (IMLS)
Pages7638-7645
Number of pages8
Volume11
ISBN (Electronic)9781510867963
StatePublished - Jan 1 2018
Event35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden
Duration: Jul 10 2018Jul 15 2018

Other

Other35th International Conference on Machine Learning, ICML 2018
CountrySweden
CityStockholm
Period7/10/187/15/18

Cite this

Sun, Q., Tan, K. M., Liu, H., & Zhang, T. (2018). Graphical nonconvex optimization via an adaptive convex relaxation. In A. Krause, & J. Dy (Eds.), 35th International Conference on Machine Learning, ICML 2018 (Vol. 11, pp. 7638-7645). International Machine Learning Society (IMLS).