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,Man-Lai Tang

Mathematics（2025）SCI 4区

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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.

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Key words

Bayesian networks,censored data,structural EM algorithm,structure learning

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【要点】：本文提出了一种适用于处理因检测限制产生的左右截断数据的 censoring Gaussian Bayesian network (GBN) 模型，并通过 Structural EM 算法进行了结构学习和参数估计的创新方法。

【方法】：作者通过扩展传统的 Gaussian Bayesian network，提出 censored GBN，并开发了 censored Structural EM (cSEM) 算法，该方法结合了蒙特卡洛采样和迭代 Markov chain Monte Carlo 算法，以解决截断数据似然非分解性问题。

【实验】：通过模拟研究和应用 cSEM 算法于单细胞数据，展示了算法在截断数据存在时网络恢复方面的优越性能，具体数据集名称在论文中未明确提及，但提及了算法实现已在 GitHub 上提供。