# Federated Causal Inference from Observational Data

arXiv: https://arxiv.org/abs/2308.13047 · HTML: https://mlsanity.com/paper/2308.13047/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 94 references that are in the map.
- First posted on arXiv 24 Aug 2023.

## Builds on (most cited first, 4 of 4)

- [Federated Learning with Non-IID Data](https://mlsanity.com/paper/1806.00582/) (2018)
- [Federated Causal Inference in Heterogeneous Observational Data](https://mlsanity.com/paper/2107.11732/) (2021)
- [MissDeepCausal: Causal Inference from Incomplete Data Using Deep Latent Variable Models](https://mlsanity.com/paper/2002.10837/) (2020)
- [Causal Transportability of Experiments on Controllable Subsets of Variables: z-Transportability](https://mlsanity.com/paper/1309.6842/) (2013)

## Built on by (most cited first, 3 of 3)

- [Collaborative Heterogeneous Causal Inference Beyond Meta-analysis](https://mlsanity.com/paper/2404.15746/) (2024)
- [Federated Inference: Toward Privacy-Preserving Collaborative and Incentivized Model Serving](https://mlsanity.com/paper/2603.02214/) (2026)
- [A Survey on Federated Causal Discovery and Inference](https://mlsanity.com/paper/2606.23741/) (2026)

## Abstract (arXiv)

Decentralized data sources are prevalent in real-world applications, posing a formidable challenge for causal inference. These sources cannot be consolidated into a single entity owing to privacy constraints. The presence of dissimilar data distributions and missing values within them can potentially introduce bias to the causal estimands. In this article, we propose a framework to estimate causal effects from decentralized data sources. The proposed framework avoid exchanging raw data among the sources, thus contributing towards privacy-preserving causal learning. Three instances of the proposed framework are introduced to estimate causal effects across a wide range of diverse scenarios within a federated setting. (1) FedCI: a Bayesian framework based on Gaussian processes for estimating causal effects from federated observational data sources. It estimates the posterior distributions of the causal effects to compute the higher-order statistics that capture the uncertainty. (2) CausalRFF: an adaptive transfer algorithm that learns the similarities among the data sources by utilizing Random Fourier Features to disentangle the loss function into multiple components, each of which is associated with a data source. It estimates the similarities among the sources through transfer coefficients, and hence requiring no prior information about the similarity measures. (3) CausalFI: a new approach for federated causal inference from incomplete data, enabling the estimation of causal effects from multiple decentralized and incomplete data sources. It accounts for the missing data under the missing at random assumption, while also estimating higher-order statistics of the causal estimands. The proposed federated framework and its instances are an important step towards a privacy-preserving causal learning model.