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

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Beilun Wang, arshdeep Sekhon, Yanjun Qi ;
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1691-1700, 2018.

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.

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