无分数等价性的基于排序的结构学习
Order-based Structure Learning without Score Equivalence
AI总结：
提出经验贝叶斯基于排序的DAG结构学习MCMC方法及自顶向下初始化算法，证明高维选择一致性，并在模拟和单细胞数据中验证其优势。
摘要：
我们提出了结构学习问题的一种经验贝叶斯表述，其中先验设定假定所有节点变量具有相同的误差方差；已知这一假定能够确保潜在因果有向无环图（DAG）的可识别性。为便于高效的后验计算，我们用最佳DAG模型的后验概率来近似每个排序的后验概率，这自然产生了一种基于排序的马尔可夫链蒙特卡洛（MCMC）算法。在允许异质误差方差的条件下，我们证明了该模型在高维环境中的强选择一致性，并从理论上研究了采样器的混合行为。此外，我们提出了一种新的迭代自顶向下算法，它能快速给出结构学习问题的近似解，并可用于初始化MCMC采样器。我们证明，在多种模拟设置下，所提方法优于其他最先进算法；论文最后以一项单细胞真实数据研究说明所提方法的实际优势。
英文摘要：
We propose an empirical Bayes formulation of the structure learning problem, where the prior specification assumes that all node variables have the same error variance, an assumption known to ensure the identifiability of the underlying causal directed acyclic graph (DAG). To facilitate efficient posterior computation, we approximate the posterior probability of each ordering by that of a best DAG model, which naturally leads to an order-based Markov chain Monte Carlo (MCMC) algorithm. Strong selection consistency for our model in high-dimensional settings is proved under a condition that allows heterogeneous error variances, and the mixing behavior of our sampler is theoretically investigated. Further, we propose a new iterative top-down algorithm, which quickly yields an approximate solution to the structure learning problem and can be used to initialize the MCMC sampler. We demonstrate that our method outperforms other state-of-the-art algorithms under various simulation settings, and conclude the paper with a single-cell real-data study illustrating practical advantages of the proposed method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
