# A Meta-Learning Approach to Bayesian Causal Discovery

arXiv: https://arxiv.org/abs/2412.16577 · HTML: https://mlsanity.com/paper/2412.16577/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 46 references that are in the map.
- First posted on arXiv 21 Dec 2024.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Neural Processes](https://mlsanity.com/paper/1807.01622/) (2018)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [A Complete Recipe for Stochastic Gradient MCMC](https://mlsanity.com/paper/1506.04696/) (2015)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Amortized Inference for Causal Structure Learning](https://mlsanity.com/paper/2205.12934/) (2022)
- [Meta-Learning Stationary Stochastic Process Prediction with Convolutional Neural Processes](https://mlsanity.com/paper/2007.01332/) (2020)
- [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)
- [ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discovery](https://mlsanity.com/paper/1902.10347/) (2019)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Variational Causal Networks: Approximate Bayesian Inference over Causal Structures](https://mlsanity.com/paper/2106.07635/) (2021)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [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)
- [Supervised Whole DAG Causal Discovery](https://mlsanity.com/paper/2006.04697/) (2020)
- [Being Bayesian about Network Structure](https://mlsanity.com/paper/1301.3856/) (2013)
- [Differentiable Multi-Target Causal Bayesian Experimental Design](https://mlsanity.com/paper/2302.10607/) (2023)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)

## Built on by (most cited first, 22 of 22)

- [Do-PFN: In-Context Learning for Causal Effect Estimation](https://mlsanity.com/paper/2506.06039/) (2025)
- [TabPFN: One Model to Rule Them All?](https://mlsanity.com/paper/2505.20003/) (2025)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Use What You Know: Causal Foundation Models with Partial Graphs](https://mlsanity.com/paper/2602.14972/) (2026)
- [CauScale: Neural Causal Discovery at Scale](https://mlsanity.com/paper/2602.08629/) (2026)
- [Does TabPFN Understand Causal Structures?](https://mlsanity.com/paper/2511.07236/) (2025)
- [Arrow: A Foundation Model for Causal Discovery](https://mlsanity.com/paper/2605.07204/) (2026)
- [Identifying Causal Direction via Variational Bayesian Compression](https://mlsanity.com/paper/2505.07503/) (2025)
- [MapPFN: Learning Causal Perturbation Maps in Context](https://mlsanity.com/paper/2601.21092/) (2026)
- [A Knowledge-Informed Pretrained Model for Causal Discovery](https://mlsanity.com/paper/2603.20842/) (2026)
- [DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanisms](https://mlsanity.com/paper/2607.11510/) (2026)
- [PerturbPFN: Probing the Limits of Synthetic Priors in Drug Perturbation Modelling](https://mlsanity.com/paper/2607.23447/) (2026)
- [MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions](https://mlsanity.com/paper/2510.22298/) (2025)
- [Transformer Is Inherently a Causal Learner](https://mlsanity.com/paper/2601.05647/) (2026)
- [DCD-PFN: A Decoupling-Aware Foundation Model for Causal Discovery](https://mlsanity.com/paper/2606.21212/) (2026)
- [Causal Foundation Models](https://mlsanity.com/paper/2609.03003/) (2026)
- [Amortising Inference and Meta-Learning Priors in Neural Networks](https://mlsanity.com/paper/2602.08782/) (2026)
- [A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs](https://mlsanity.com/paper/2605.06288/) (2026)
- [PRIM: Meta-Learned Bayesian Root Cause Analysis](https://mlsanity.com/paper/2605.08786/) (2026)
- [PACER: Acyclic Causal Discovery from Large-Scale Interventional Data](https://mlsanity.com/paper/2605.15353/) (2026)
- [SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2608.04930/) (2026)
- [Demistifying Data and Simulator Assumptions in Supervised Causal Discovery](https://mlsanity.com/paper/2609.37446/) (2026)

## Abstract (arXiv)

Discovering a unique causal structure is difficult due to both inherent identifiability issues, and the consequences of finite data. As such, uncertainty over causal structures, such as those obtained from a Bayesian posterior, are often necessary for downstream tasks. Finding an accurate approximation to this posterior is challenging, due to the large number of possible causal graphs, as well as the difficulty in the subproblem of finding posteriors over the functional relationships of the causal edges. Recent works have used meta-learning to view the problem of estimating the maximum a-posteriori causal graph as supervised learning. Yet, these methods are limited when estimating the full posterior as they fail to encode key properties of the posterior, such as correlation between edges and permutation equivariance with respect to nodes. Further, these methods also cannot reliably sample from the posterior over causal structures. To address these limitations, we propose a Bayesian meta learning model that allows for sampling causal structures from the posterior and encodes these key properties. We compare our meta-Bayesian causal discovery against existing Bayesian causal discovery methods, demonstrating the advantages of directly learning a posterior over causal structure.