# Module-based regularization improves Gaussian graphical models when observing noisy data

arXiv: https://arxiv.org/abs/2303.16796 · HTML: https://mlsanity.com/paper/2303.16796/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Network reconstruction and community detection from dynamics](https://mlsanity.com/paper/1903.10833/) (2019)
- [Estimating Psychological Networks and their Accuracy: A Tutorial Paper](https://mlsanity.com/paper/1604.08462/) (2016)
- [Mapping higher-order network flows in memory and multilayer networks with Infomap](https://mlsanity.com/paper/1706.04792/) (2017)
- [The Cluster Graphical Lasso for improved estimation of Gaussian graphical models](https://mlsanity.com/paper/1307.5339/) (2013)
- [Exploring the limits of community detection strategies in complex networks](https://mlsanity.com/paper/1306.4149/) (2013)
- [Exploring the solution landscape enables more reliable network community detection](https://mlsanity.com/paper/1905.11230/) (2019)

## Built on by (most cited first, 1 of 1)

- [Reliable data clustering with Bayesian community detection](https://mlsanity.com/paper/2510.15013/) (2025)

## Abstract (arXiv)

Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using Gaussian graphical models, requiring regularization to sparsify the models. Acknowledging that the modular structure of the inferred network is often studied, we suggest module-based regularization to balance under- and overfitting. Compared with the graphical lasso, a standard approach using the Gaussian log-likelihood for estimating the regularization strength, this approach better recovers and infers modular structure in noisy synthetic and real data. The module-based regularization technique improves the usefulness of Gaussian graphical models in the many applications where they are employed.