# Towards Practical Federated Causal Structure Learning

arXiv: https://arxiv.org/abs/2306.09433 · HTML: https://mlsanity.com/paper/2306.09433/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 19 of 19)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Personalized Federated Learning with Moreau Envelopes](https://mlsanity.com/paper/2006.08848/) (2020)
- [FedML: A Research Library and Benchmark for Federated Machine Learning](https://mlsanity.com/paper/2007.13518/) (2020)
- [Federated Learning for Edge Networks: Resource Optimization and Incentive Mechanism](https://mlsanity.com/paper/1911.05642/) (2019)
- [Federated Learning With Quantized Global Model Updates](https://mlsanity.com/paper/2006.10672/) (2020)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Theory Refinement on Bayesian Networks](https://mlsanity.com/paper/1303.5709/) (2013)
- [Local Constraint-Based Causal Discovery under Selection Bias](https://mlsanity.com/paper/2203.01848/) (2022)
- [Differentially Private Estimation of Heterogeneous Causal Effects](https://mlsanity.com/paper/2202.11043/) (2022)
- [Private Causal Inference](https://mlsanity.com/paper/1512.05469/) (2015)
- [Local Private Hypothesis Testing: Chi-Square Tests](https://mlsanity.com/paper/1709.07155/) (2017)
- [Towards practical differentially private causal graph discovery](https://mlsanity.com/paper/2006.08598/) (2020)
- [Federated Data Analytics: A Study on Linear Models](https://mlsanity.com/paper/2206.07786/) (2022)
- [XInsight: eXplainable Data Analysis Through The Lens of Causality](https://mlsanity.com/paper/2207.12718/) (2022)
- [Analysis and Optimal Edge Assignment For Hierarchical Federated Learning on Non-IID Data](https://mlsanity.com/paper/2012.05622/) (2020)
- [FED-chi2: Privacy Preserving Federated Correlation Test](https://mlsanity.com/paper/2105.14618/) (2021)
- [Private independence testing across two parties](https://mlsanity.com/paper/2207.03652/) (2022)

## Built on by (most cited first, 9 of 9)

- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [FedGES: A Federated Learning Approach for BN Structure Learning](https://mlsanity.com/paper/2502.01538/) (2025)
- [Towards Practical Multi-label Causal Discovery in High-Dimensional Event Sequences via One-Shot Graph Aggregation](https://mlsanity.com/paper/2509.19112/) (2025)
- [Regret-Based Federated Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2512.23626/) (2025)
- [Federated Causal Discovery Across Heterogeneous Datasets under Latent Confounding](https://mlsanity.com/paper/2603.05149/) (2026)
- [Differentially Private and Federated Structure Learning in Bayesian Networks](https://mlsanity.com/paper/2512.01708/) (2025)
- [Fed-CausalDiff: Decoupled Synchronization for Federated Do-Simulation and Policy Evaluation](https://mlsanity.com/paper/2606.22510/) (2026)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)
- [Federated Causal Discovery via Regression-Directed Cumulants](https://mlsanity.com/paper/2609.03705/) (2026)

## Abstract (arXiv)

Understanding causal relations is vital in scientific discovery. The process of causal structure learning involves identifying causal graphs from observational data to understand such relations. Usually, a central server performs this task, but sharing data with the server poses privacy risks. Federated learning can solve this problem, but existing solutions for federated causal structure learning make unrealistic assumptions about data and lack convergence guarantees. FedC2SL is a federated constraint-based causal structure learning scheme that learns causal graphs using a federated conditional independence test, which examines conditional independence between two variables under a condition set without collecting raw data from clients. FedC2SL requires weaker and more realistic assumptions about data and offers stronger resistance to data variability among clients. FedPC and FedFCI are the two variants of FedC2SL for causal structure learning in causal sufficiency and causal insufficiency, respectively. The study evaluates FedC2SL using both synthetic datasets and real-world data against existing solutions and finds it demonstrates encouraging performance and strong resilience to data heterogeneity among clients.