Bayesian causal discovery aims to infer the posterior distribution over
causal models from observed data, quantifying epistemic uncertainty and
benefiting downstream tasks. However, computational challenges arise due to
joint inference over combinatorial space of Directed Acyclic Graphs (DAGs) and
nonlinear functions. Despite recent progress towards efficient posterior
inference over DAGs, existing methods are either limited to variational
inference on node permutation matrices for linear causal models, leading to
compromised inference accuracy, or continuous relaxation of adjacency matrices
constrained by a DAG regularizer, which cannot ensure resulting graphs are
DAGs. In this work, we introduce a scalable Bayesian causal discovery framework
based on stochastic gradient Markov Chain Monte Carlo (SG-MCMC) that overcomes
these limitations. Our approach directly samples DAGs from the posterior
without requiring any DAG regularization, simultaneously draws function
parameter samples and is applicable to both linear and nonlinear causal models.
To enable our approach, we derive a novel equivalence to the permutation-based
DAG learning, which opens up possibilities of using any relaxed gradient
estimator defined over permutations. To our knowledge, this is the first
framework applying gradient-based MCMC sampling for causal discovery. Empirical
evaluations on synthetic and real-world datasets demonstrate our approach's
effectiveness compared to state-of-the-art baselines.

基于随机梯度马尔可夫链蒙特卡洛 (SG-MCMC) 的可伸缩贝叶斯因果关系发现框架，无需任何有向无环图 (DAG) 正则化约束，直接从后验中采样有向无环图 (DAG)，同时绘制函数参数样本，适用于线性和非线性因果模型。基于合法的等价关系，我们首次应用基于梯度的 MCMC 采样用于因果关系发现。通过对合成数据集和真实世界数据集的实证评估，展示了我们方法与最先进基准模型的有效性。