# DiBS: Differentiable Bayesian Structure Learning

arXiv: https://arxiv.org/abs/2105.11839 · HTML: https://mlsanity.com/paper/2105.11839/

## Key facts

- Cited by 106 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 74 references that are in the map.
- First posted on arXiv 25 May 2021.

## Builds on (most cited first, 29 of 29)

- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [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)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [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)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [D-VAE: A Variational Autoencoder for Directed Acyclic Graphs](https://mlsanity.com/paper/1904.11088/) (2019)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks](https://mlsanity.com/paper/2010.09133/) (2020)
- [Learning Gaussian Networks](https://mlsanity.com/paper/1302.6808/) (2013)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Causal Discovery Toolbox: Uncover causal relationships in Python](https://mlsanity.com/paper/1903.02278/) (2019)
- [Structural Agnostic Modeling: Adversarial Learning of Causal Graphs](https://mlsanity.com/paper/1803.04929/) (2018)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [On the Convergence of Continuous Constrained Optimization for Structure Learning](https://mlsanity.com/paper/2011.11150/) (2020)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [Partition MCMC for inference on acyclic digraphs](https://mlsanity.com/paper/1504.05006/) (2015)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [Optimal experimental design via Bayesian optimization: active causal structure learning for Gaussian process networks](https://mlsanity.com/paper/1910.03962/) (2019)

## Built on by (most cited first, 30 of 106)

- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [A theory of continuous generative flow networks](https://mlsanity.com/paper/2301.12594/) (2023)
- [Deep End-to-end Causal Inference](https://mlsanity.com/paper/2202.02195/) (2022)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Identifiability Guarantees for Causal Disentanglement from Soft Interventions](https://mlsanity.com/paper/2307.06250/) (2023)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Network](https://mlsanity.com/paper/2305.19366/) (2023)
- [Interventions, Where and How? Experimental Design for Causal Models at Scale](https://mlsanity.com/paper/2203.02016/) (2022)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [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)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [Active Learning for Optimal Intervention Design in Causal Models](https://mlsanity.com/paper/2209.04744/) (2022)
- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets](https://mlsanity.com/paper/2302.04178/) (2023)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (2024)
- [GeneDisco: A Benchmark for Experimental Design in Drug Discovery](https://mlsanity.com/paper/2110.11875/) (2021)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [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)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Benchmarking and Explaining Large Language Model-based Code Generation: A Causality-Centric Approach](https://mlsanity.com/paper/2310.06680/) (2023)
- [Computably Continuous Reinforcement-Learning Objectives are PAC-learnable](https://mlsanity.com/paper/2303.05518/) (2023)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [ML4C: Seeing Causality Through Latent Vicinity](https://mlsanity.com/paper/2110.00637/) (2021)
- [Toward Falsifying Causal Graphs Using a Permutation-Based Test](https://mlsanity.com/paper/2305.09565/) (2023)

## Abstract (arXiv)

Bayesian structure learning allows inferring Bayesian network structure from data while reasoning about the epistemic uncertainty -- a key element towards enabling active causal discovery and designing interventions in real world systems. In this work, we propose a general, fully differentiable framework for Bayesian structure learning (DiBS) that operates in the continuous space of a latent probabilistic graph representation. Contrary to existing work, DiBS is agnostic to the form of the local conditional distributions and allows for joint posterior inference of both the graph structure and the conditional distribution parameters. This makes our formulation directly applicable to posterior inference of complex Bayesian network models, e.g., with nonlinear dependencies encoded by neural networks. Using DiBS, we devise an efficient, general purpose variational inference method for approximating distributions over structural models. In evaluations on simulated and real-world data, our method significantly outperforms related approaches to joint posterior inference.