# Distributed Learning of Generalized Linear Causal Networks

arXiv: https://arxiv.org/abs/2201.09194 · HTML: https://mlsanity.com/paper/2201.09194/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 74 references that are in the map.
- First posted on arXiv 23 Jan 2022.

## Builds on (most cited first, 18 of 18)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [Causal Structure Learning](https://mlsanity.com/paper/1706.09141/) (2017)
- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Penalized Estimation of Directed Acyclic Graphs From Discrete Data](https://mlsanity.com/paper/1403.2310/) (2014)
- [Learning Large-Scale Bayesian Networks with the sparsebn Package](https://mlsanity.com/paper/1703.04025/) (2017)
- [Optimizing regularized Cholesky score for order-based learning of Bayesian networks](https://mlsanity.com/paper/1904.12360/) (2019)
- [Causal network learning with non-invertible functional relationships](https://mlsanity.com/paper/2004.09646/) (2020)
- [Bayesian network marker selection via the thresholded graph Laplacian Gaussian prior](https://mlsanity.com/paper/1810.00274/) (2018)

## Built on by (most cited first, 13 of 13)

- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [Federated Causality Learning with Explainable Adaptive Optimization](https://mlsanity.com/paper/2312.05540/) (2023)
- [Markov Equivalence and Consistency in Differentiable Structure Learning](https://mlsanity.com/paper/2410.06163/) (2024)
- [FedGES: A Federated Learning Approach for BN Structure Learning](https://mlsanity.com/paper/2502.01538/) (2025)
- [Regret-Based Federated Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2512.23626/) (2025)
- [Federated Causal Discovery From Interventions](https://mlsanity.com/paper/2211.03846/) (2022)
- [Federated Causal Representation Learning in State-Space Systems for Decentralized Counterfactual Reasoning](https://mlsanity.com/paper/2602.19414/) (2026)
- [Toward Federated Multimodal Graph Foundation Models: A Topology-Aware Multimodal Alignment Framework](https://mlsanity.com/paper/2607.15687/) (2026)
- [Drift-Aware Federated Learning: A Causal Perspective](https://mlsanity.com/paper/2503.09116/) (2025)
- [Federated Spectral Graph Transformers Meet Neural Ordinary Differential Equations for Non-IID Graphs](https://mlsanity.com/paper/2504.11808/) (2025)
- [From Privacy to Trust in the Agentic Era: A Taxonomy of Challenges in Trustworthy Federated Learning Through the Lens of Trust Report 2.0](https://mlsanity.com/paper/2507.15796/) (2025)
- [Differentiable Structure Learning and Causal Discovery for General Binary Data](https://mlsanity.com/paper/2509.21658/) (2025)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)

## Abstract (arXiv)

We consider the task of learning causal structures from data stored on multiple machines, and propose a novel structure learning method called distributed annealing on regularized likelihood score (DARLS) to solve this problem. We model causal structures by a directed acyclic graph that is parameterized with generalized linear models, so that our method is applicable to various types of data. To obtain a high-scoring causal graph, DARLS simulates an annealing process to search over the space of topological sorts, where the optimal graphical structure compatible with a sort is found by a distributed optimization method. This distributed optimization relies on multiple rounds of communication between local and central machines to estimate the optimal structure. We establish its convergence to a global optimizer of the overall score that is computed on all data across local machines. To the best of our knowledge, DARLS is the first distributed method for learning causal graphs with such theoretical guarantees. Through extensive simulation studies, DARLS has shown competing performance against existing methods on distributed data, and achieved comparable structure learning accuracy and test-data likelihood with competing methods applied to pooled data across all local machines. In a real-world application for modeling protein-DNA binding networks with distributed ChIP-Sequencing data, DARLS also exhibits higher predictive power than other methods, demonstrating a great advantage in estimating causal networks from distributed data.