HiBCD: Scalable Bayesian Causal Discovery for High-Dimensional Data

Bayesian causal structure learning aims to infer causal graphs from observational data based on Bayesian posterior inference. However, the combinatorial nature of the graph space makes these methods computationally intractable for high-dimensional settings where the number of variables is large. To address this challenge, we propose HiBCD, a divide-and-conquer Bayesian causal discovery method for high-dimensional variables. The method first employs a hierarchical weighted sampling strategy to partition the high-dimensional variable set into several smaller, manageable subsets. Subsequently, for each subset, we infer a posterior over local causal orderings using a pre-trained meta estimator. The meta estimator features a symmetry-aware encoder and a Bayesian scoring head and is trained via a variational objective to ensure robustness to latent confounders. Finally, these local orderings are iteratively aggregated into a global causal topology, from which the full causal graph can be efficiently recovered. Experiments demonstrate that HiBCD significantly outperforms previous Bayesian causal discovery methods on large-scale data in terms of structural accuracy, while maintaining highly scalable computational efficiency.