Gaussian Graphical Model Selection Using Graph Compression

Conditional independence between variables in Gaussian graphical models (also known as Gaussian Markov random fields) is represented by the conditional independence graph, \(G\). Most approaches for inferring conditional independence graph rely on the penalized log-likelihood, where a regularization hyperparameter, \(\lambda\), controls the preference for either a sparsely or densely connected solution. In this article, we present a method for selecting \(\lambda\) based on the minimum description length (MDL) principle. Our approach improves upon previous methods by better accounting for \(G\) using our novel graph coders. Experiments on known Gaussian graphical models demonstrate that our approach has a higher F1 score in recovering the true conditional independence graph than existing methods, especially when the number of observations is small compared to the number of variables. We also applied our method to a real-world electrocardiogram (ECG) dataset to investigate the inferred conditional independence graph in healthy subjects versus a group of subjects with Kawasaki disease. Finally, we used the learned conditional independence graphs for the classification of healthy subjects versus those with Kawasaki disease.