# Node-Based Learning of Multiple Gaussian Graphical Models

arXiv: https://arxiv.org/abs/1303.5145 · HTML: https://mlsanity.com/paper/1303.5145/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2013.

## Built on by (most cited first, 26 of 26)

- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Multi-task Learning of Order-Consistent Causal Graphs](https://mlsanity.com/paper/2111.02545/) (2021)
- [Dynamic Multi-Network Mining of Tensor Time Series](https://mlsanity.com/paper/2402.11773/) (2024)
- [On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series](https://mlsanity.com/paper/2111.07897/) (2021)
- [uGLAD: Sparse graph recovery by optimizing deep unrolled networks](https://mlsanity.com/paper/2205.11610/) (2022)
- [Sparse Graph Learning Under Laplacian-Related Constraints](https://mlsanity.com/paper/2111.08161/) (2021)
- [Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series](https://mlsanity.com/paper/2204.13824/) (2022)
- [Mining of Switching Sparse Networks for Missing Value Imputation in Multivariate Time Series](https://mlsanity.com/paper/2409.09930/) (2024)
- [Learning High-Dimensional Differential Graphs From Multi-Attribute Data](https://mlsanity.com/paper/2312.03761/) (2023)
- [Multiview Graph Learning with Consensus Graph](https://mlsanity.com/paper/2401.13769/) (2024)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Distributed Estimation of Sparse Inverse Covariances](https://mlsanity.com/paper/2109.12020/) (2021)
- [Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation](https://mlsanity.com/paper/2205.00007/) (2022)
- [Efficient Inference of Spatially-varying Gaussian Markov Random Fields with Applications in Gene Regulatory Networks](https://mlsanity.com/paper/2206.10174/) (2022)
- [Solution Path of Time-varying Markov Random Fields with Discrete Regularization](https://mlsanity.com/paper/2307.13750/) (2023)
- [Scalable Regularised Joint Mixture Models](https://mlsanity.com/paper/2205.01486/) (2022)
- [A Graphical Model for Fusing Diverse Microbiome Data](https://mlsanity.com/paper/2208.09934/) (2022)
- [The non-overlapping statistical approximation to overlapping group lasso](https://mlsanity.com/paper/2211.09221/) (2022)
- [Detecting and Ranking Causal Anomalies in End-to-End Complex System](https://mlsanity.com/paper/2301.07281/) (2023)
- [Robust Online Covariance and Sparse Precision Estimation Under Arbitrary Data Corruption](https://mlsanity.com/paper/2309.08884/) (2023)
- [Clusterpath Gaussian Graphical Modeling](https://mlsanity.com/paper/2407.00644/) (2024)
- [Efficient learning of differential network in multi-source non-paranormal graphical models](https://mlsanity.com/paper/2410.02496/) (2024)
- [Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees](https://mlsanity.com/paper/2512.12435/) (2025)
- [Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso](https://mlsanity.com/paper/2602.08197/) (2026)
- [TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matching](https://mlsanity.com/paper/2607.16894/) (2026)

## Abstract (arXiv)

We consider the problem of estimating high-dimensional Gaussian graphical models corresponding to a single set of variables under several distinct conditions. This problem is motivated by the task of recovering transcriptional regulatory networks on the basis of gene expression data {containing heterogeneous samples, such as different disease states, multiple species, or different developmental stages}. We assume that most aspects of the conditional dependence networks are shared, but that there are some structured differences between them. Rather than assuming that similarities and differences between networks are driven by individual edges, we take a node-based approach, which in many cases provides a more intuitive interpretation of the network differences. We consider estimation under two distinct assumptions: (1) differences between the K networks are due to individual nodes that are perturbed across conditions, or (2) similarities among the K networks are due to the presence of common hub nodes that are shared across all K networks. Using a row-column overlap norm penalty function, we formulate two convex optimization problems that correspond to these two assumptions. We solve these problems using an alternating direction method of multipliers algorithm, and we derive a set of necessary and sufficient conditions that allows us to decompose the problem into independent subproblems so that our algorithm can be scaled to high-dimensional settings. Our proposal is illustrated on synthetic data, a webpage data set, and a brain cancer gene expression data set.