We propose a joint order-based scoring framework for causal structure learning of directed acyclic graph (DAG) models under heterogeneous data settings. We show that leveraging heterogeneity improves the accuracy of causal ordering estimation. In the most favorable case, the causal ordering is identifiable up to two permutations. Building on this framework, we propose an order-based Bayesian method for Gaussian DAG models and establish its theoretical properties in the high-dimensional regime. For posterior inference over the space of orderings, we introduce a random-to-random (R2R) proposal neighborhood for the Metropolis-Hastings algorithm, which is theoretically motivated and exhibits efficient mixing behavior. Simulation studies confirm the strong empirical performance of the proposed method, and an application to single-nucleus RNA sequencing data from major depressive disorder demonstrates practical utility.

翻译：我们提出了一种联合序评分框架，用于在异质性数据设置下对结构因果学习中的有向无环图（DAG）模型进行因果结构学习。研究表明，利用数据异质性能够提高因果序估计的准确性；在最有利的情况下，因果序可识别至两个排列以内。基于此框架，我们进一步提出了一种适用于高斯DAG模型的贝叶斯序方法，并建立了其在高维条件下的理论性质。针对序空间的其后验推断，我们引入了一种随机到随机（R2R）邻域提案方法，用于Metropolis-Hastings算法中，该方法具备理论动机且展现出高效的混合行为。模拟研究证实了所提方法在实证中具有优异表现，而对重度抑郁症单细胞核RNA测序数据的应用进一步证明了其实际效用。