In this paper, we introduce a novel MCMC sampler, PARNI-DAG, for a fully-Bayesian approach to the problem of structure learning under observational data. Under the assumption of causal sufficiency, the algorithm allows for approximate sampling directly from the posterior distribution on Directed Acyclic Graphs (DAGs). PARNI-DAG performs efficient sampling of DAGs via locally informed, adaptive random neighborhood proposal that results in better mixing properties. In addition, to ensure better scalability with the number of nodes, we couple PARNI-DAG with a pre-tuning procedure of the sampler's parameters that exploits a skeleton graph derived through some constraint-based or scoring-based algorithms. Thanks to these novel features, PARNI-DAG quickly converges to high-probability regions and is less likely to get stuck in local modes in the presence of high correlation between nodes in high-dimensional settings. After introducing the technical novelties in PARNI-DAG, we empirically demonstrate its mixing efficiency and accuracy in learning DAG structures on a variety of experiments.

翻译：本文提出一种新型MCMC采样器PARNI-DAG，用于解决观测数据下的完全贝叶斯结构学习问题。在因果充分性假设下，该算法可直接从有向无环图（DAG）的后验分布中进行近似采样。PARNI-DAG通过局部信息驱动的自适应随机邻域提议机制实现DAG的高效采样，从而获得更优的混合特性。此外，为确保算法随节点数量扩展的可伸缩性，我们将其与参数预调优流程相结合——该流程利用基于约束或评分算法导出的骨架图信息。凭借这些创新特性，PARNI-DAG能快速收敛至高概率区域，并在高维场景下节点高度相关时降低陷入局部模态的风险。在阐述PARNI-DAG的技术创新后，我们通过系列实验实证证明了其在DAG结构学习中的混合效率与准确性。