Fast and Scalable Learning of Sparse Changes in High-Dimensional Gaussian Graphical Model Structure
This addresses a computationally expensive bottleneck in change detection for high-dimensional dependency structures, with applications in fields like neuroscience.
The paper tackles the problem of estimating sparse changes between two high-dimensional Gaussian Graphical Models, proposing DIFFEE which achieves the same asymptotic convergence rates as state-of-the-art methods while offering a faster closed-form solution. Experimental results show strong performance improvements and significant computational benefits on synthetic and brain connectivity data.
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.