# Joint Gaussian Graphical Model Estimation: A Survey

arXiv: https://arxiv.org/abs/2110.10281 · HTML: https://mlsanity.com/paper/2110.10281/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 108 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 30 of 36)

- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [The Dynamics of Functional Brain Networks: Integrated Network States during Cognitive Function](https://mlsanity.com/paper/1511.02976/) (2015)
- [Asymptotic normality and optimalities in estimation of large Gaussian graphical models](https://mlsanity.com/paper/1309.6024/) (2013)
- [High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models](https://mlsanity.com/paper/1804.00778/) (2018)
- [Estimating Time-varying Brain Connectivity Networks from Functional MRI Time Series](https://mlsanity.com/paper/1310.3863/) (2013)
- [Integrative Factor Regression and Its Inference for Multimodal Data Analysis](https://mlsanity.com/paper/1911.04056/) (2019)
- [Differential Network Analysis via the Lasso Penalized D-Trace Loss](https://mlsanity.com/paper/1511.09188/) (2015)
- [Simultaneous Clustering and Estimation of Heterogeneous Graphical Models](https://mlsanity.com/paper/1611.09391/) (2016)
- [Estimating Time-Varying Graphical Models](https://mlsanity.com/paper/1804.03811/) (2018)
- [Direct Estimation of Differential Functional Graphical Models](https://mlsanity.com/paper/1910.09701/) (2019)
- [Joint Estimation of Multiple Graphical Models from High Dimensional Time Series](https://mlsanity.com/paper/1311.0219/) (2013)
- [Confidence intervals for high-dimensional inverse covariance estimation](https://mlsanity.com/paper/1403.6752/) (2014)
- [Time-dependent spatially varying graphical models, with application to brain fMRI data analysis](https://mlsanity.com/paper/1711.03701/) (2017)
- [Two-sample inference for high-dimensional Markov networks](https://mlsanity.com/paper/1905.00466/) (2019)
- [Estimating Differential Latent Variable Graphical Models with Applications to Brain Connectivity](https://mlsanity.com/paper/1909.05892/) (2019)
- [Differential Network Analysis: A Statistical Perspective](https://mlsanity.com/paper/2003.04235/) (2020)
- [Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso](https://mlsanity.com/paper/1512.06171/) (2015)
- [Testing for Differences in Gaussian Graphical Models: Applications to Brain Connectivity](https://mlsanity.com/paper/1512.08643/) (2015)
- [Bayesian Joint Modeling of Multiple Brain Functional Networks](https://mlsanity.com/paper/1708.02123/) (2017)
- [ROCKET: Robust Confidence Intervals via Kendall's Tau for Transelliptical Graphical Models](https://mlsanity.com/paper/1502.07641/) (2015)
- [Joint Estimation of Precision Matrices in Heterogeneous Populations](https://mlsanity.com/paper/1601.00142/) (2016)
- [Simultaneous Inference for Pairwise Graphical Models with Generalized Score Matching](https://mlsanity.com/paper/1905.06261/) (2019)
- [Statistical Inference for Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2007.07448/) (2020)
- [Inference for Sparse Conditional Precision Matrices](https://mlsanity.com/paper/1412.7638/) (2014)
- [On Joint Estimation of Gaussian Graphical Models for Spatial and Temporal Data](https://mlsanity.com/paper/1507.01933/) (2015)
- [Bayesian inference for multiple Gaussian graphical models with application to metabolic association networks](https://mlsanity.com/paper/1603.06358/) (2016)
- [Estimating Multiple Precision Matrices with Cluster Fusion Regularization](https://mlsanity.com/paper/2003.00371/) (2020)
- [Targeted Fused Ridge Estimation of Inverse Covariance Matrices from Multiple High-Dimensional Data Classes](https://mlsanity.com/paper/1509.07982/) (2015)

## Built on by (most cited first, 10 of 10)

- [Joint Network Topology Inference via a Shared Graphon Model](https://mlsanity.com/paper/2209.08223/) (2022)
- [Latent Multimodal Functional Graphical Model Estimation](https://mlsanity.com/paper/2210.17237/) (2022)
- [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)
- [Estimation of partially known Gaussian graphical models with score-based structural priors](https://mlsanity.com/paper/2401.14340/) (2024)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Spectral Differential Network Analysis for High-Dimensional Time Series](https://mlsanity.com/paper/2412.07905/) (2024)
- [Exploration of the search space of Gaussian graphical models for paired data](https://mlsanity.com/paper/2303.05561/) (2023)
- [Learning Networks from Wide-Sense Stationary Stochastic Processes](https://mlsanity.com/paper/2412.03768/) (2024)
- [Co-Hub Node Based Multiview Graph Learning with Theoretical Guarantees](https://mlsanity.com/paper/2512.12435/) (2025)

## Abstract (arXiv)

Graphs from complex systems often share a partial underlying structure across domains while retaining individual features. Thus, identifying common structures can shed light on the underlying signal, for instance, when applied to scientific discoveries or clinical diagnoses. Furthermore, growing evidence shows that the shared structure across domains boosts the estimation power of graphs, particularly for high-dimensional data. However, building a joint estimator to extract the common structure may be more complicated than it seems, most often due to data heterogeneity across sources. This manuscript surveys recent work on statistical inference of joint Gaussian graphical models, identifying model structures that fit various data generation processes. Simulations under different data generation processes are implemented with detailed discussions on the choice of models.