# Towards Scalable Bayesian Learning of Causal DAGs

arXiv: https://arxiv.org/abs/2010.00684 · HTML: https://mlsanity.com/paper/2010.00684/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2020.

## Built on by (most cited first, 30 of 33)

- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Simultaneous Missing Value Imputation and Structure Learning with Groups](https://mlsanity.com/paper/2110.08223/) (2021)
- [Tractable Uncertainty for Structure Learning](https://mlsanity.com/paper/2204.14170/) (2022)
- [CoLiDE: Concomitant Linear DAG Estimation](https://mlsanity.com/paper/2310.02895/) (2023)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Interactive Causal Structure Discovery in Earth System Sciences](https://mlsanity.com/paper/2107.01126/) (2021)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [Scalable Differentiable Causal Discovery in the Presence of Latent Confounders with Skeleton Posterior (Extended Version)](https://mlsanity.com/paper/2406.10537/) (2024)
- [Learning Latent Structural Causal Models](https://mlsanity.com/paper/2210.13583/) (2022)
- [The interventional Bayesian Gaussian equivalent score for Bayesian causal inference with unknown soft interventions](https://mlsanity.com/paper/2205.02602/) (2022)
- [A Bayesian Take on Gaussian Process Networks](https://mlsanity.com/paper/2306.11380/) (2023)
- [ProDAG: Projected Variational Inference for Directed Acyclic Graphs](https://mlsanity.com/paper/2405.15167/) (2024)
- [CMVAE: Causal Meta VAE for Unsupervised Meta-Learning](https://mlsanity.com/paper/2302.09731/) (2023)
- [Benchmarking Bayesian Causal Discovery Methods for Downstream Treatment Effect Estimation](https://mlsanity.com/paper/2307.04988/) (2023)
- [Bayesian Causal Inference with Gaussian Process Networks](https://mlsanity.com/paper/2402.00623/) (2024)
- [Scalable Bayesian Network Structure Learning with Splines](https://mlsanity.com/paper/2110.14626/) (2021)
- [The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networks](https://mlsanity.com/paper/2112.09036/) (2021)
- [Concomitant DAG Learning: On the Roles of Noise Adaptivity, Sparsity, and Non-negativity](https://mlsanity.com/paper/2605.23537/) (2026)
- [Latent Variable Models for Bayesian Causal Discovery](https://mlsanity.com/paper/2207.05723/) (2022)
- [Scalable Variational Causal Discovery Unconstrained by Acyclicity](https://mlsanity.com/paper/2407.04992/) (2024)
- [Bayesian Approach to Linear Bayesian Networks](https://mlsanity.com/paper/2311.15610/) (2023)
- [Scaling Up Bayesian DAG Sampling](https://mlsanity.com/paper/2510.25254/) (2025)
- [A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs](https://mlsanity.com/paper/2605.06288/) (2026)

## Abstract (arXiv)

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks, which enables efficient approximate sampling from the graph posterior, provided that each node is assigned a small number K of candidate parents. We present algorithmic techniques to significantly reduce the space and time requirements, which make the use of substantially larger values of K feasible. Furthermore, we investigate the problem of selecting the candidate parents per node so as to maximize the covered posterior mass. Finally, we combine our sampling method with a novel Bayesian approach for estimating causal effects in linear Gaussian DAG models. Numerical experiments demonstrate the performance of our methods in detecting ancestor-descendant relations, and in causal effect estimation our Bayesian method is shown to outperform previous approaches.