Order-based structure learning without score equivalence

• 成果类型: Article; Early Access
• 署名作者: Chang, Hyunwoong; Cai, James J.; Zhou, Quan
• 署名单位: Texas A&M University System; Texas A&M University College Station; Texas A&M University System; Texas A&M University College Station
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad052
• 发表日期: 2023
• 关键词: Bayesian networks; Graphical Models; structure mcmc; selection; Consistency; likelihood; DISCOVERY

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. To facilitate efficient posterior computation, we approximate the posterior probability of each ordering by that of a best directed acyclic graph model, which naturally leads to an order-based Markov chain Monte Carlo algorithm. Strong selection consistency for our model in high-dimensional settings is proved under a condition that allows heterogeneous error variances, and the mixing behaviour of our sampler is theoretically investigated. Furthermore, 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 Markov chain Monte Carlo 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.