# Robust sparse Gaussian graphical modeling

arXiv: https://arxiv.org/abs/1508.05571 · HTML: https://mlsanity.com/paper/1508.05571/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2015.

## Built on by (most cited first, 3 of 3)

- [Minimizing robust density power-based divergences for general parametric density models](https://mlsanity.com/paper/2307.05251/) (2023)
- [Adaptively Robust and Sparse K-means Clustering](https://mlsanity.com/paper/2407.06945/) (2024)
- [Data-driven configuration tuning of glmnet for balancing accuracy and computational efficiency](https://mlsanity.com/paper/2602.17922/) (2026)

## Abstract (arXiv)

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the L1 penalty for learning a high-dimensional graphical model. However, the penalized maximum likelihood procedure is sensitive to outliers. To overcome this problem, we introduce a robust estimation procedure based on the γ-divergence. The proposed method has a redescending property, which is known as a desirable property in robust statistics. The parameter estimation procedure is constructed using the Majorize-Minimization algorithm, which guarantees that the objective function monotonically decreases at each iteration. Extensive simulation studies showed that our procedure performed much better than the existing methods, in particular, when the contamination ratio was large. Two real data analyses were carried out to illustrate the usefulness of our proposed procedure.