发表机构
Ferdowsi University of Mashhad（马什哈德 Ferdowsi 大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出NPN-DAG-HS，一种结合非参数正态族与马蹄形收缩的贝叶斯半参数DAG模型，无需估计单调变换即可处理非高斯数据，在高维下具有理论保证，并在模拟和真实数据中优于高斯方法。
AI 中文摘要
有向无环图（DAG）的贝叶斯结构学习对于高维因果发现至关重要，然而现有方法大多假设多元高斯数据，这通常会被呈现重尾、偏斜或有界支撑的测量数据所违背。我们通过引入NPN-DAG-HS来解决这一问题，这是一种完全贝叶斯半参数DAG模型，通过扩展秩似然将非参数正态族与Cholesky非对角线上的马蹄形收缩相结合。该方法无需估计即可处理任意未知的单调边际变换，同时保留精确零收缩和条件共轭后验，便于在大维度中进行实际推断。我们的方法使用部分折叠的Metropolis-within-Gibbs采样器，该采样器增广秩似然高斯副本，并交替进行基于分数的DAG移动和马蹄形吉布斯更新。理论上，在高维情形下（$p \to \infty$ 且 $\log p / n \to 0$），我们建立了以 $\sqrt{(s_0+p)\log p/n}$ 速率的后验收缩、强骨架选择一致性，以及针对光滑总因果效应泛函的参数化Bernstein-von Mises定理，从而得到可信区间的渐近频率校准。模拟实验证实，我们的方法优于高斯基线和标准频率学派学习器。应用于急性髓系白血病数据集时，它恢复了一个稀疏、可解释的网络，修剪了高斯分析所声明的无支撑边，体现了我们半参数松弛的价值。
英文摘要
Bayesian structure learning of directed acyclic graphs (DAGs) is central to high-dimensional causal discovery, yet existing methods mostly assume multivariate Gaussian data, which is routinely violated by measurements displaying heavy tails, skewness, or bounded support. We address this by introducing NPN-DAG-HS, a fully Bayesian semiparametric DAG model coupling the nonparanormal family with horseshoe shrinkage on Cholesky off-diagonals via an extended-rank likelihood. This handles arbitrary unknown monotone marginal transformations without estimating them, preserving exact-zero shrinkage and conditionally conjugate posteriors for practical inference in large dimensions. Our method uses a partially collapsed Metropolis-within-Gibbs sampler that augments rank-likelihood Gaussian copies and alternates score-based DAG moves with horseshoe Gibbs updates. Theoretically, in the high-dimensional regime ($p \to \infty$ with $\log p / n \to 0$), we establish posterior contraction at the rate $\sqrt{(s_0+p)\log p/n}$, strong skeleton selection consistency, and a parametric Bernstein-von Mises theorem for smooth total causal-effect functionals, yielding asymptotic frequentist calibration of credible intervals. Simulations confirm our method outperforms Gaussian baselines and standard frequentist learners. Applied to an acute myeloid leukaemia dataset, it recovers a sparse, interpretable network, pruning unsupported edges declared by Gaussian analyses and illustrating the value of our semiparametric relaxation.
