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October 2016 Innovated scalable efficient estimation in ultra-large Gaussian graphical models
Yingying Fan, Jinchi Lv
Ann. Statist. 44(5): 2098-2126 (October 2016). DOI: 10.1214/15-AOS1416

Abstract

Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient estimation (ISEE) for estimating large precision matrix. Motivated by the innovated transformation, we convert the original problem into that of large covariance matrix estimation. The suggested method combines the strengths of recent advances in high-dimensional sparse modeling and large covariance matrix estimation. Compared to existing approaches, our method is scalable and can deal with much larger precision matrices with simple tuning. Under mild regularity conditions, we establish that this procedure can recover the underlying graphical structure with significant probability and provide efficient estimation of link strengths. Both computational and theoretical advantages of the procedure are evidenced through simulation and real data examples.

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Yingying Fan. Jinchi Lv. "Innovated scalable efficient estimation in ultra-large Gaussian graphical models." Ann. Statist. 44 (5) 2098 - 2126, October 2016. https://doi.org/10.1214/15-AOS1416

Information

Received: 1 May 2015; Revised: 1 November 2015; Published: October 2016
First available in Project Euclid: 12 September 2016

zbMATH: 1349.62206
MathSciNet: MR3546445
Digital Object Identifier: 10.1214/15-AOS1416

Subjects:
Primary: 62F12 , 62H12
Secondary: 62J05

Keywords: big data , efficiency , Gaussian graphical model , precision matrix , scalability , Sparsity

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 5 • October 2016
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