Fast and Scalable Learning of Sparse Changes in High-Dimensional Gaussian Graphical Model Structure

TL;DR

This paper introduces DIFFEE, a fast, scalable method for estimating sparse changes in high-dimensional Gaussian Graphical Models, achieving comparable accuracy to existing methods with significantly improved computational efficiency.

Contribution

The paper presents DIFFEE, a novel closed-form estimator for differential networks in high-dimensional GGMs, enabling faster computation without sacrificing statistical accuracy.

Findings

DIFFEE achieves the same asymptotic convergence rates as more complex estimators.

DIFFEE outperforms baselines in synthetic datasets in accuracy and speed.

Real-world brain connectivity data analysis demonstrates DIFFEE's practical effectiveness.

Abstract

We focus on the problem of estimating the change in the dependency structures of two $p$-dimensional Gaussian Graphical models (GGMs). Previous studies for sparse change estimation in GGMs involve expensive and difficult non-smooth optimization. We propose a novel method, DIFFEE for estimating DIFFerential networks via an Elementary Estimator under a high-dimensional situation. DIFFEE is solved through a faster and closed form solution that enables it to work in large-scale settings. We conduct a rigorous statistical analysis showing that surprisingly DIFFEE achieves the same asymptotic convergence rates as the state-of-the-art estimators that are much more difficult to compute. Our experimental results on multiple synthetic datasets and one real-world data about brain connectivity show strong performance improvements over baselines, as well as significant computational benefits.