# Causal Discovery with Heterogeneous Observational Data

arXiv: https://arxiv.org/abs/2201.12392 · HTML: https://mlsanity.com/paper/2201.12392/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2022.

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

- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [Effective Causal Discovery under Identifiable Heteroscedastic Noise Model](https://mlsanity.com/paper/2312.12844/) (2023)
- [Directed Cyclic Graph for Causal Discovery from Multivariate Functional Data](https://mlsanity.com/paper/2310.20537/) (2023)
- [Learning Causal Graphs at Scale: A Foundation Model Approach](https://mlsanity.com/paper/2506.18285/) (2025)
- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments](https://mlsanity.com/paper/2506.11756/) (2025)
- [ExMAG: Learning of Maximally Ancestral Graphs](https://mlsanity.com/paper/2503.08245/) (2025)
- [Interpretable Clustering with Adaptive Heterogeneous Causal Structure Learning in Mixed Observational Data](https://mlsanity.com/paper/2509.04415/) (2025)
- [Consistent Bayesian causal discovery for structural equation models with equal error variances](https://mlsanity.com/paper/2509.15197/) (2025)
- [Invariant Causal Prediction with Local Models](https://mlsanity.com/paper/2401.05218/) (2024)
- [Covariate-dependent Graphical Model Estimation via Neural Networks with Statistical Guarantees](https://mlsanity.com/paper/2504.16356/) (2025)

## Abstract (arXiv)

We consider the problem of causal discovery (structure learning) from heterogeneous observational data. Most existing methods assume a homogeneous sampling scheme, which leads to misleading conclusions when violated in many applications. To this end, we propose a novel approach that exploits data heterogeneity to infer possibly cyclic causal structures from causally insufficient systems. The core idea is to model the direct causal effects as functions of exogenous covariates that properly explain data heterogeneity. We investigate structure identifiability properties of the proposed model. Structure learning is carried out in a fully Bayesian fashion, which provides natural uncertainty quantification. We demonstrate its utility through extensive simulations and a real-world application.