# Causal Structure Discovery from Distributions Arising from Mixtures of DAGs

arXiv: https://arxiv.org/abs/2001.11940 · HTML: https://mlsanity.com/paper/2001.11940/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2020.

## Built on by (most cited first, 24 of 24)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Federated Causal Discovery from Heterogeneous Data](https://mlsanity.com/paper/2402.13241/) (2024)
- [A Distance Covariance-based Kernel for Nonlinear Causal Clustering in Heterogeneous Populations](https://mlsanity.com/paper/2106.03480/) (2021)
- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [Disentangling Mixtures of Unknown Causal Interventions](https://mlsanity.com/paper/2210.03242/) (2022)
- [Collaborative Causal Discovery with Atomic Interventions](https://mlsanity.com/paper/2106.03028/) (2021)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [Tackling Non-Stationarity in Reinforcement Learning via Causal-Origin Representation](https://mlsanity.com/paper/2306.02747/) (2023)
- [Causal Discovery in Mixtures of Populations](https://mlsanity.com/paper/2311.07454/) (2023)
- [Interventional Causal Discovery in a Mixture of DAGs](https://mlsanity.com/paper/2406.08666/) (2024)
- [CCSL: A Causal Structure Learning Method from Multiple Unknown Environments](https://mlsanity.com/paper/2111.09666/) (2021)
- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphs](https://mlsanity.com/paper/2510.06735/) (2025)
- [NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters](https://mlsanity.com/paper/2111.01104/) (2021)
- [Causal Modeling in Multi-Context Systems: Distinguishing Multiple Context-Specific Causal Graphs which Account for Observational Support](https://mlsanity.com/paper/2410.20405/) (2024)
- [Covariate Dependent Mixture of Bayesian Networks](https://mlsanity.com/paper/2501.05745/) (2025)
- [Learning Causal Structure Distributions for Robust Planning](https://mlsanity.com/paper/2508.06742/) (2025)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)
- [Fine-Grained System Identification of Nonlinear Neural Circuits](https://mlsanity.com/paper/2106.05400/) (2021)
- [Learning Mixtures of Unknown Causal Interventions](https://mlsanity.com/paper/2411.00213/) (2024)
- [Heterogeneous Ordinal Structure Learning with Bayesian Nonparametric Complexity Discovery](https://mlsanity.com/paper/2605.04191/) (2026)
- [Detecting Changes in Causal Dependence with Kernels and Copulas](https://mlsanity.com/paper/2605.05809/) (2026)
- [Structure Learning on Clustered Data](https://mlsanity.com/paper/2607.08238/) (2026)

## Abstract (arXiv)

We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a "union" of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.