# Minimal I-MAP MCMC for Scalable Structure Discovery in Causal DAG Models

arXiv: https://arxiv.org/abs/1803.05554 · HTML: https://mlsanity.com/paper/1803.05554/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

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

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Tractable Uncertainty for Structure Learning](https://mlsanity.com/paper/2204.14170/) (2022)
- [Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGs](https://mlsanity.com/paper/2310.05655/) (2023)
- [Greedy equivalence search for nonparametric graphical models](https://mlsanity.com/paper/2406.17228/) (2024)
- [BCDAG: An R package for Bayesian structure and Causal learning of Gaussian DAGs](https://mlsanity.com/paper/2201.12003/) (2022)
- [Identifiability of the minimum-trace directed acyclic graph and hill climbing algorithms without strict local optima under weakly increasing error variances](https://mlsanity.com/paper/2508.05706/) (2025)
- [Large-Scale Bayesian Causal Discovery with Interventional Data](https://mlsanity.com/paper/2510.01562/) (2025)
- [Leveraging heterogeneity for identifiability: Bayesian order-based learning of multiple DAGs](https://mlsanity.com/paper/2605.15639/) (2026)

## Abstract (arXiv)

Learning a Bayesian network (BN) from data can be useful for decision-making or discovering causal relationships. However, traditional methods often fail in modern applications, which exhibit a larger number of observed variables than data points. The resulting uncertainty about the underlying network as well as the desire to incorporate prior information recommend a Bayesian approach to learning the BN, but the highly combinatorial structure of BNs poses a striking challenge for inference. The current state-of-the-art methods such as order MCMC are faster than previous methods but prevent the use of many natural structural priors and still have running time exponential in the maximum indegree of the true directed acyclic graph (DAG) of the BN. We here propose an alternative posterior approximation based on the observation that, if we incorporate empirical conditional independence tests, we can focus on a high-probability DAG associated with each order of the vertices. We show that our method allows the desired flexibility in prior specification, removes timing dependence on the maximum indegree and yields provably good posterior approximations; in addition, we show that it achieves superior accuracy, scalability, and sampler mixing on several datasets.