Leveraging heterogeneity for identifiability: Bayesian order-based learning of multiple DAGs

TL;DR

This paper introduces a Bayesian order-based framework for causal structure learning in heterogeneous data, improving identifiability and estimation accuracy of DAG models, with theoretical guarantees and practical applications.

Contribution

It presents a novel order-based scoring framework and Bayesian method for Gaussian DAGs that leverage heterogeneity, with theoretical analysis and efficient inference algorithms.

Findings

Heterogeneity improves causal ordering accuracy.

Causal ordering is identifiable up to two permutations in favorable cases.

Simulation and real data demonstrate strong empirical performance.

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 (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.