Model Selection With Graphical Neighbour Information

TL;DR

This paper introduces Graphical Neighbour Information, a new model selection criterion for high-dimensional graphical models that outperforms existing methods in accuracy and efficiency, with theoretical backing and simulation validation.

Contribution

The paper proposes a novel, oracle-performing model score criterion for high-dimensional graphical model selection that is computationally efficient and theoretically validated.

Findings

Outperforms existing high-dimensional model selection methods in simulations

Offers closed-form computation reducing inference costs

Demonstrates oracle performance in high-dimensional settings

Abstract

Accurate model selection is a fundamental requirement for statistical analysis. In many real-world applications of graphical modelling, correct model structure identification is the ultimate objective. Standard model validation procedures such as information theoretic scores and cross validation have demonstrated poor performance in the high dimensional setting. Specialised methods such as EBIC, StARS and RIC have been developed for the explicit purpose of high-dimensional Gaussian graphical model selection. We present a novel model score criterion, Graphical Neighbour Information. This method demonstrates oracle performance in high-dimensional model selection, outperforming the current state-of-the-art in our simulations. The Graphical Neighbour Information criterion has the additional advantage of efficient, closed-form computability, sparing the costly inference of multiple models on data subsamples. We provide a theoretical analysis of the method and benchmark simulations versus the current state of the art.