Composite likelihood estimation of sparse Gaussian graphical models with symmetry

TL;DR

This paper introduces a composite likelihood approach for estimating sparse Gaussian graphical models with symmetry constraints, providing a computationally efficient and consistent method that maintains sparsity and symmetry, demonstrated through simulations and biological data analysis.

Contribution

The paper proposes a novel penalized composite likelihood method for sparse Gaussian graphical models with symmetry, ensuring consistency and the ORACLE property.

Findings

Method achieves consistent estimation under symmetry constraints.

Simulation studies validate the effectiveness of the approach.

Application to biological data demonstrates practical utility.

Abstract

In this article, we discuss the composite likelihood estimation of sparse Gaussian graphical models. When there are symmetry constraints on the concentration matrix or partial correlation matrix, the likelihood estimation can be computational intensive. The composite likelihood offers an alternative formulation of the objective function and yields consistent estimators. When a sparse model is considered, the penalized composite likelihood estimation can yield estimates satisfying both the symmetry and sparsity constraints and possess ORACLE property. Application of the proposed method is demonstrated through simulation studies and a network analysis of a biological data set.