# Federated Causality Learning with Explainable Adaptive Optimization

arXiv: https://arxiv.org/abs/2312.05540 · HTML: https://mlsanity.com/paper/2312.05540/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 9 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [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)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Secure Federated Matrix Factorization](https://mlsanity.com/paper/1906.05108/) (2019)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [Towards Federated Bayesian Network Structure Learning with Continuous Optimization](https://mlsanity.com/paper/2110.09356/) (2021)
- [Federated Causal Inference in Heterogeneous Observational Data](https://mlsanity.com/paper/2107.11732/) (2021)
- [Distributed Learning of Generalized Linear Causal Networks](https://mlsanity.com/paper/2201.09194/) (2022)

## Built on by (most cited first, 11 of 11)

- [Causal Explainability of Machine Learning in Heart Failure Prediction from Electronic Health Records](https://mlsanity.com/paper/2506.03068/) (2025)
- [Regret-Based Federated Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2512.23626/) (2025)
- [Federated Causal Inference in Healthcare: Methods, Challenges, and Applications](https://mlsanity.com/paper/2505.02238/) (2025)
- [Interpretable Clustering with Adaptive Heterogeneous Causal Structure Learning in Mixed Observational Data](https://mlsanity.com/paper/2509.04415/) (2025)
- [Federated Causal Representation Learning in State-Space Systems for Decentralized Counterfactual Reasoning](https://mlsanity.com/paper/2602.19414/) (2026)
- [Drift-Aware Federated Learning: A Causal Perspective](https://mlsanity.com/paper/2503.09116/) (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)
- [Federated Learning of Nonlinear Temporal Dynamics with Graph Attention-based Cross-Client Interpretability](https://mlsanity.com/paper/2602.13485/) (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)
- [SeaCausal-FL: Federated Fuzzy Causal Learning for Maritime IoT Fault Diagnosis and Counterfactual Reasoning](https://mlsanity.com/paper/2609.06257/) (2026)

## Abstract (arXiv)

Discovering the causality from observational data is a crucial task in various scientific domains. With increasing awareness of privacy, data are not allowed to be exposed, and it is very hard to learn causal graphs from dispersed data, since these data may have different distributions. In this paper, we propose a federated causal discovery strategy (FedCausal) to learn the unified global causal graph from decentralized heterogeneous data. We design a global optimization formula to naturally aggregate the causal graphs from client data and constrain the acyclicity of the global graph without exposing local data. Unlike other federated causal learning algorithms, FedCausal unifies the local and global optimizations into a complete directed acyclic graph (DAG) learning process with a flexible optimization objective. We prove that this optimization objective has a high interpretability and can adaptively handle homogeneous and heterogeneous data. Experimental results on synthetic and real datasets show that FedCausal can effectively deal with non-independently and identically distributed (non-iid) data and has a superior performance.