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

arXiv: https://arxiv.org/abs/1710.11223 · HTML: https://mlsanity.com/paper/1710.11223/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Oct 2017.

## Built on by (most cited first, 2 of 2)

- [Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees](https://mlsanity.com/paper/2102.03585/) (2021)
- [Solution Path of Time-varying Markov Random Fields with Discrete Regularization](https://mlsanity.com/paper/2307.13750/) (2023)

## Abstract (arXiv)

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.