Abstract 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 proposal neighborhood for the Metropolis–Hastings algorithm, which is theoretically motivated and exhibits efficient mixing behavior. Simulation studies confirm the strong empirical performance, and its application to single-nucleus RNA sequencing data from major depressive disorder demonstrates practical utility.
Photos
Participants: 15