# Federated Causal Discovery from Heterogeneous Data

arXiv: https://arxiv.org/abs/2402.13241 · HTML: https://mlsanity.com/paper/2402.13241/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 63 references that are in the map.
- First posted on arXiv 20 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [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 from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [A Survey on Homomorphic Encryption Schemes: Theory and Implementation](https://mlsanity.com/paper/1704.03578/) (2017)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [On the Error of Random Fourier Features](https://mlsanity.com/paper/1506.02785/) (2015)
- [Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discovery](https://mlsanity.com/paper/1702.03877/) (2017)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [DAGs with No Curl: An Efficient DAG Structure Learning Approach](https://mlsanity.com/paper/2106.07197/) (2021)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Neuropathic Pain Diagnosis Simulator for Causal Discovery Algorithm Evaluation](https://mlsanity.com/paper/1906.01732/) (2019)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Causal Structure Discovery from Distributions Arising from Mixtures of DAGs](https://mlsanity.com/paper/2001.11940/) (2020)
- [FedDAG: Federated DAG Structure Learning](https://mlsanity.com/paper/2112.03555/) (2021)
- [Distributed Learning of Generalized Linear Causal Networks](https://mlsanity.com/paper/2201.09194/) (2022)
- [Causal Discovery with Heterogeneous Observational Data](https://mlsanity.com/paper/2201.12392/) (2022)
- [Towards Privacy-Aware Causal Structure Learning in Federated Setting](https://mlsanity.com/paper/2211.06919/) (2022)
- [Towards Practical Federated Causal Structure Learning](https://mlsanity.com/paper/2306.09433/) (2023)
- [Discovery and Visualization of Nonstationary Causal Models](https://mlsanity.com/paper/1509.08056/) (2015)

## Built on by (most cited first, 15 of 15)

- [Causal Representation Learning from Multimodal Biomedical Observations](https://mlsanity.com/paper/2411.06518/) (2024)
- [Applications of Generative AI (GAI) for Mobile and Wireless Networking: A Survey](https://mlsanity.com/paper/2405.20024/) (2024)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [A Conditional Independence Test in the Presence of Discretization](https://mlsanity.com/paper/2404.17644/) (2024)
- [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)
- [Interventional Causal Structure Discovery over Graphical Models with Convergence and Optimality Guarantees](https://mlsanity.com/paper/2408.04819/) (2024)
- [Federated Causal Representation Learning in State-Space Systems for Decentralized Counterfactual Reasoning](https://mlsanity.com/paper/2602.19414/) (2026)
- [Consistency evaluation of benchmarks used for causal discovery](https://mlsanity.com/paper/2606.01789/) (2026)
- [PersonaX: Multimodal Datasets with LLM-Inferred Behavior Traits](https://mlsanity.com/paper/2509.11362/) (2025)
- [Federated Concept-Based Models: Interpretable models with distributed supervision](https://mlsanity.com/paper/2602.04093/) (2026)
- [Causal Discovery Should Embrace the Wisdom of the Crowd](https://mlsanity.com/paper/2603.02678/) (2026)
- [Distributed Dynamic Invariant Causal Prediction in Environmental Time Series](https://mlsanity.com/paper/2603.02902/) (2026)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)
- [Operationalising Relative Causal Knowledge: Backbone Identifiability from Private Reports on a Shared Outcome](https://mlsanity.com/paper/2608.10664/) (2026)

## Abstract (arXiv)

Conventional causal discovery methods rely on centralized data, which is inconsistent with the decentralized nature of data in many real-world situations. This discrepancy has motivated the development of federated causal discovery (FCD) approaches. However, existing FCD methods may be limited by their potentially restrictive assumptions of identifiable functional causal models or homogeneous data distributions, narrowing their applicability in diverse scenarios. In this paper, we propose a novel FCD method attempting to accommodate arbitrary causal models and heterogeneous data. We first utilize a surrogate variable corresponding to the client index to account for the data heterogeneity across different clients. We then develop a federated conditional independence test (FCIT) for causal skeleton discovery and establish a federated independent change principle (FICP) to determine causal directions. These approaches involve constructing summary statistics as a proxy of the raw data to protect data privacy. Owing to the nonparametric properties, FCIT and FICP make no assumption about particular functional forms, thereby facilitating the handling of arbitrary causal models. We conduct extensive experiments on synthetic and real datasets to show the efficacy of our method. The code is available at https://github.com/lokali/FedCDH.git.