Graph Coding for Model Selection and Anomaly Detection in Gaussian Graphical Models

TL;DR

This paper extends the description length framework to Gaussian graphical models, enabling more rigorous model selection and anomaly detection using universal graph coding, with demonstrated improvements on synthetic and ECG data.

Contribution

It introduces a novel approach to model selection and anomaly detection in Gaussian graphical models using universal graph coding methods.

Findings

Improved accuracy in graph model selection.

Effective anomaly detection in ECG data.

Superior performance over existing methods.

Abstract

A classic application of description length is for model selection with the minimum description length (MDL) principle. The focus of this paper is to extend description length for data analysis beyond simple model selection and sequences of scalars. More specifically, we extend the description length for data analysis in Gaussian graphical models. These are powerful tools to model interactions among variables in a sequence of i.i.d Gaussian data in the form of a graph. Our method uses universal graph coding methods to accurately account for model complexity, and therefore provide a more rigorous approach for graph model selection. The developed method is tested with synthetic and electrocardiogram (ECG) data to find the graph model and anomaly in Gaussian graphical models. The experiments show that our method gives better performance compared to commonly used methods.