Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm

Ping-Feng Xu, Shanyi Lin, Qian-Zhen Zheng () and Man-Lai Tang ()
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Ping-Feng Xu: Academy for Advanced Interdisciplinary Studies & Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, China
Shanyi Lin: School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China
Qian-Zhen Zheng: College of Education, Zhejiang Normal University, Jinhua 321004, China
Man-Lai Tang: Department of Physics, Astronomy and Mathematics, School of Physics, Engineering & Computer Science, University of Hertfordshire, Hertfordshire AL10 9AB, UK

Mathematics, 2025, vol. 13, issue 9, 1-20

Abstract: A Bayesian network offers powerful knowledge representations for independence, conditional independence and causal relationships among variables in a given domain. Despite its wide application, the detection limits of modern measurement technologies make the use of the Bayesian networks theoretically unfounded, even when the assumption of a multivariate Gaussian distribution is satisfied. In this paper, we introduce the censored Gaussian Bayesian network (GBN), an extension of GBNs designed to handle left- and right-censored data caused by instrumental detection limits. We further propose the censored Structural Expectation-Maximization (cSEM) algorithm, an iterative score-and-search framework that integrates Monte Carlo sampling in the E-step for efficient expectation computation and employs the iterative Markov chain Monte Carlo (MCMC) algorithm in the M-step to refine the network structure and parameters. This approach addresses the non-decomposability challenge of censored-data likelihoods. Through simulation studies, we illustrate the superior performance of the cSEM algorithm compared to the existing competitors in terms of network recovery when censored data exist. Finally, the proposed cSEM algorithm is applied to single-cell data with censoring to uncover the relationships among variables. The implementation of the cSEM algorithm is available on GitHub.

Keywords: Bayesian networks; censored data; structural EM algorithm; structure learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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