Innovated scalable efficient estimation in ultra-large Gaussian graphical models

TL;DR

This paper introduces a new scalable method called ISEE for estimating large Gaussian graphical models by transforming the problem into covariance matrix estimation, enabling efficient recovery of structure and link strengths in ultra-large settings.

Contribution

The paper proposes the innovated scalable efficient estimation (ISEE) method, which is scalable, simple to tune, and effective for ultra-large precision matrices, advancing high-dimensional graphical model estimation.

Findings

Method successfully recovers graphical structure with high probability.

Efficient estimation of link strengths demonstrated.

Scalable approach handles much larger matrices than existing methods.

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.