# High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models

arXiv: https://arxiv.org/abs/1804.00778 · HTML: https://mlsanity.com/paper/1804.00778/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2018.

## Built on by (most cited first, 12 of 12)

- [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)
- [Joint inference of multiple graphs with hidden variables from stationary graph signals](https://mlsanity.com/paper/2110.03666/) (2021)
- [CCSL: A Causal Structure Learning Method from Multiple Unknown Environments](https://mlsanity.com/paper/2111.09666/) (2021)
- [Estimation of partially known Gaussian graphical models with score-based structural priors](https://mlsanity.com/paper/2401.14340/) (2024)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Graphon-aided Joint Estimation of Multiple Graphs](https://mlsanity.com/paper/2202.05686/) (2022)
- [Structural transfer learning of non-Gaussian DAG](https://mlsanity.com/paper/2310.10239/) (2023)
- [Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal Kernel Clustering](https://mlsanity.com/paper/2501.11622/) (2025)
- [Leveraging heterogeneity for identifiability: Bayesian order-based learning of multiple DAGs](https://mlsanity.com/paper/2605.15639/) (2026)
- [Causal Intelligence for Constraint-Aware Intervention Design to Induce State Transitions](https://mlsanity.com/paper/2605.29008/) (2026)

## Abstract (arXiv)

We consider the problem of jointly estimating multiple related directed acyclic graph (DAG) models based on high-dimensional data from each graph. This problem is motivated by the task of learning gene regulatory networks based on gene expression data from different tissues, developmental stages or disease states. We prove that under certain regularity conditions, the proposed ℓ0-penalized maximum likelihood estimator converges in Frobenius norm to the adjacency matrices consistent with the data-generating distributions and has the correct sparsity. In particular, we show that this joint estimation procedure leads to a faster convergence rate than estimating each DAG model separately. As a corollary, we also obtain high-dimensional consistency results for causal inference from a mix of observational and interventional data. For practical purposes, we propose jointGES consisting of Greedy Equivalence Search (GES) to estimate the union of all DAG models followed by variable selection using lasso to obtain the different DAGs, and we analyze its consistency guarantees. The proposed method is illustrated through an analysis of simulated data as well as epithelial ovarian cancer gene expression data.