  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.
