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.

本研究介绍了一种新颖的 MCMC 采样器 PARNI-DAG，用于在观测数据下进行结构学习的完全贝叶斯方法。算法假设因果充分性，允许从有向无环图（DAGs）的后验分布中直接进行近似采样。PARNI-DAG 通过局部启发式、自适应的随机邻域提议有效地采样 DAGs，从而改善混合特性。此外，为了更好地适应节点数量的伸缩性，我们将 PARNI-DAG 与通过某些基于约束或基于评分的算法导出的骨架图预调参数的过程相结合。由于这些新颖的特性，PARNI-DAG 在高维设置中在存在高相关性的节点之间不容易陷入局部模态，能快速收敛到高概率区域。在介绍 PARNI-DAG 的技术创新后，我们通过各种实验证明其混合效率和结构学习准确性。