Model Selection With Graphical Neighbour Information
This addresses the challenge of accurate model selection in high-dimensional graphical modeling for statistical analysis, representing a strong specific gain rather than a foundational advancement.
The paper tackles the problem of high-dimensional Gaussian graphical model selection, where standard methods perform poorly, by introducing the Graphical Neighbour Information criterion, which achieves oracle performance and outperforms state-of-the-art methods in simulations while being computationally efficient.
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.