# Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes

arXiv: https://arxiv.org/abs/2211.02763 · HTML: https://mlsanity.com/paper/2211.02763/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 48 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 25 of 25)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [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)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Learning to Induce Causal Structure](https://mlsanity.com/paper/2204.04875/) (2022)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [Learning Neural Causal Models with Active Interventions](https://mlsanity.com/paper/2109.02429/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Being Bayesian about Network Structure](https://mlsanity.com/paper/1301.3856/) (2013)
- [Tractable Uncertainty for Structure Learning](https://mlsanity.com/paper/2204.14170/) (2022)
- [On the Equivalence of Causal Models](https://mlsanity.com/paper/1304.1108/) (2013)
- [Learning Latent Structural Causal Models](https://mlsanity.com/paper/2210.13583/) (2022)

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

- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Better Training of GFlowNets with Local Credit and Incomplete Trajectories](https://mlsanity.com/paper/2302.01687/) (2023)
- [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)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [GFlowNet-EM for learning compositional latent variable models](https://mlsanity.com/paper/2302.06576/) (2023)
- [Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets](https://mlsanity.com/paper/2305.17010/) (2023)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [Stochastic Generative Flow Networks](https://mlsanity.com/paper/2302.09465/) (2023)
- [Distributional GFlowNets with Quantile Flows](https://mlsanity.com/paper/2302.05793/) (2023)
- [Adaptive teachers for amortized samplers](https://mlsanity.com/paper/2410.01432/) (2024)
- [Passive learning of active causal strategies in agents and language models](https://mlsanity.com/paper/2305.16183/) (2023)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Graph Neural Flows for Unveiling Systemic Interactions Among Irregularly Sampled Time Series](https://mlsanity.com/paper/2410.14030/) (2024)
- [Order-Preserving GFlowNets](https://mlsanity.com/paper/2310.00386/) (2023)
- [Delta-AI: Local objectives for amortized inference in sparse graphical models](https://mlsanity.com/paper/2310.02423/) (2023)
- [Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2510.04792/) (2025)
- [Compositional Flows for 3D Molecule and Synthesis Pathway Co-design](https://mlsanity.com/paper/2504.08051/) (2025)
- [Challenges and Considerations in the Evaluation of Bayesian Causal Discovery](https://mlsanity.com/paper/2406.03209/) (2024)
- [Sample Efficient Bayesian Learning of Causal Graphs from Interventions](https://mlsanity.com/paper/2410.20089/) (2024)
- [Generative Flow Networks for Precise Reward-Oriented Active Learning on Graphs](https://mlsanity.com/paper/2304.11989/) (2023)
- [Differentiable Bayesian Structure Learning with Acyclicity Assurance](https://mlsanity.com/paper/2309.01392/) (2023)
- [Multi-Agent Continuous Control with Generative Flow Networks](https://mlsanity.com/paper/2408.06920/) (2024)
- [Possible Principles for Aligned Structure Learning Agents](https://mlsanity.com/paper/2410.00258/) (2024)
- [gfnx: Fast and Scalable Library for Generative Flow Networks in JAX](https://mlsanity.com/paper/2511.16592/) (2025)
- [Enhance Eye Disease Detection using Learnable Probabilistic Discrete Latents in Machine Learning Architectures](https://mlsanity.com/paper/2402.16865/) (2024)
- [Bifurcated Generative Flow Networks](https://mlsanity.com/paper/2406.01901/) (2024)
- [Learning Causal Structure Distributions for Robust Planning](https://mlsanity.com/paper/2508.06742/) (2025)
- [Planning-Augmented Sampling with Early Guidance for High-Reward Discovery](https://mlsanity.com/paper/2510.00805/) (2025)
- [SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2608.04930/) (2026)

## Abstract (arXiv)

Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that define the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.