Fast and Scalable Learning of Sparse Changes in High-Dimensional Gaussian Graphical Model Structure
Beilun Wang, arshdeep Sekhon, Yanjun Qi
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.
BibTeX
@InProceedings{pmlr-v84-wang18f,
title = {Fast and Scalable Learning of Sparse Changes in High-Dimensional Gaussian Graphical Model Structure},
author = {Wang, Beilun and Sekhon, arshdeep and Qi, Yanjun},
booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
pages = {1691--1700},
year = {2018},
editor = {Storkey, Amos and Perez-Cruz, Fernando},
volume = {84},
series = {Proceedings of Machine Learning Research},
month = {09--11 Apr},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v84/wang18f/wang18f.pdf},
url = {https://proceedings.mlr.press/v84/wang18f.html},
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.}
}