# Causal Discovery via Bayesian Optimization

arXiv: https://arxiv.org/abs/2501.14997 · HTML: https://mlsanity.com/paper/2501.14997/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 90 references that are in the map.
- First posted on arXiv 25 Jan 2025.

## Builds on (most cited first, 30 of 44)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/1906.04477/) (2019)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Batched Large-scale Bayesian Optimization in High-dimensional Spaces](https://mlsanity.com/paper/1706.01445/) (2017)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Recent Advances in Bayesian Optimization](https://mlsanity.com/paper/2206.03301/) (2022)
- [Diffusion Models for Causal Discovery via Topological Ordering](https://mlsanity.com/paper/2210.06201/) (2022)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [gCastle: A Python Toolbox for Causal Discovery](https://mlsanity.com/paper/2111.15155/) (2021)
- [Ordering-Based Causal Discovery with Reinforcement Learning](https://mlsanity.com/paper/2105.06631/) (2021)

## Built on by (most cited first, 1 of 1)

- [Arrow: A Foundation Model for Causal Discovery](https://mlsanity.com/paper/2605.07204/) (2026)

## Abstract (arXiv)

Existing score-based methods for directed acyclic graph (DAG) learning from observational data struggle to recover the causal graph accurately and sample-efficiently. To overcome this, in this study, we propose DrBO (DAG recovery via Bayesian Optimization)-a novel DAG learning framework leveraging Bayesian optimization (BO) to find high-scoring DAGs. We show that, by sophisticatedly choosing the promising DAGs to explore, we can find higher-scoring ones much more efficiently. To address the scalability issues of conventional BO in DAG learning, we replace Gaussian Processes commonly employed in BO with dropout neural networks, trained in a continual manner, which allows for (i) flexibly modeling the DAG scores without overfitting, (ii) incorporation of uncertainty into the estimated scores, and (iii) scaling with the number of evaluations. As a result, DrBO is computationally efficient and can find the accurate DAG in fewer trials and less time than existing state-of-the-art methods. This is demonstrated through an extensive set of empirical evaluations on many challenging settings with both synthetic and real data. Our implementation is available at https://github.com/baosws/DrBO.