Order-based structure learning for zero-inflated count data under data heterogeneity

We propose a structure learning method for directed acyclic graph (DAG) models of zero-inflated multivariate count data. Although causal structure learning with zero-inflated Poisson models is identifiable, existing algorithms rely on local search over the DAG space, leading to poor scalability and a tendency to converge to suboptimal solutions. To address these limitations, we develop a novel order-based scoring framework that searches over variable orderings rather than directly over DAGs. Building on this framework, we further extend the method to multiple heterogeneous datasets by identifying a shared variable ordering while allowing each dataset to have its own edge set. We implement a stochastic hill climbing algorithm with a random-to-random (R2R) proposal operator to efficiently explore the ordering space. Simulation studies show that the proposed method outperforms competing approaches and improves graph estimation accuracy under increasing heterogeneity when a shared causal ordering is preserved. We apply the method to single-nucleus RNA sequencing data from a major depressive disorder study.