# Learning Mixtures of DAG Models

arXiv: https://arxiv.org/abs/1301.7415 · HTML: https://mlsanity.com/paper/1301.7415/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jan 2013.

## Built on by (most cited first, 10 of 10)

- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)
- [Semiparametric Bayesian Networks](https://mlsanity.com/paper/2109.03008/) (2021)
- [Disentangling Mixtures of Unknown Causal Interventions](https://mlsanity.com/paper/2210.03242/) (2022)
- [Interventional Causal Discovery in a Mixture of DAGs](https://mlsanity.com/paper/2406.08666/) (2024)
- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters](https://mlsanity.com/paper/2111.01104/) (2021)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)
- [Learning Mixtures of Unknown Causal Interventions](https://mlsanity.com/paper/2411.00213/) (2024)
- [A Unified Framework for Structure-Aware Clustering and Heterogeneous Causal Graph Learning](https://mlsanity.com/paper/2605.19313/) (2026)

## Abstract (arXiv)

We describe computationally efficient methods for learning mixtures in which each component is a directed acyclic graphical model (mixtures of DAGs or MDAGs). We argue that simple search-and-score algorithms are infeasible for a variety of problems, and introduce a feasible approach in which parameter and structure search is interleaved and expected data is treated as real data. Our approach can be viewed as a combination of (1) the Cheeseman--Stutz asymptotic approximation for model posterior probability and (2) the Expectation--Maximization algorithm. We evaluate our procedure for selecting among MDAGs on synthetic and real examples.