Graphical Exponential Screening

TL;DR

This paper introduces graphical Exponential Screening (gES), an aggregation method for estimating precision matrices in high-dimensional Gaussian graphical models, balancing error and sparsity, with strong theoretical and empirical performance.

Contribution

The paper proposes a novel aggregation estimator, gES, that combines multiple graph-based estimators to improve precision matrix estimation in high dimensions.

Findings

gES achieves risk comparable to the best single-graph estimator.

Numerical experiments show gES outperforms existing methods.

gES effectively balances estimation accuracy and sparsity.

Abstract

In high dimensions we propose and analyze an aggregation estimator of the precision matrix for Gaussian graphical models. This estimator, called graphical Exponential Screening (gES), linearly combines a suitable set of individual estimators with different underlying graphs, and balances the estimation error and sparsity. We study the risk of this aggregation estimator and show that it is comparable to that of the best estimator based on a single graph, chosen by an oracle. Numerical performance of our method is investigated using both simulated and real datasets, in comparison with some state-of-art estimation procedures.