Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm
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 theoreticall...
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/9/1482 |
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| author | Ping-Feng Xu Shanyi Lin Qian-Zhen Zheng Man-Lai Tang |
| author_facet | Ping-Feng Xu Shanyi Lin Qian-Zhen Zheng Man-Lai Tang |
| author_sort | Ping-Feng Xu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d3e86002fd1d4b7fb8a453b571945292 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-d3e86002fd1d4b7fb8a453b5719452922025-08-20T03:49:22ZengMDPI AGMathematics2227-73902025-04-01139148210.3390/math13091482Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM AlgorithmPing-Feng Xu0Shanyi Lin1Qian-Zhen Zheng2Man-Lai Tang3Academy for Advanced Interdisciplinary Studies & Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, ChinaSchool of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, ChinaCollege of Education, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Physics, Astronomy and Mathematics, School of Physics, Engineering & Computer Science, University of Hertfordshire, Hertfordshire AL10 9AB, UKA 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.https://www.mdpi.com/2227-7390/13/9/1482Bayesian networkscensored datastructural EM algorithmstructure learning |
| spellingShingle | Ping-Feng Xu Shanyi Lin Qian-Zhen Zheng Man-Lai Tang Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm Mathematics Bayesian networks censored data structural EM algorithm structure learning |
| title | Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm |
| title_full | Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm |
| title_fullStr | Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm |
| title_full_unstemmed | Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm |
| title_short | Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm |
| title_sort | learning gaussian bayesian network from censored data subject to limit of detection by the structural em algorithm |
| topic | Bayesian networks censored data structural EM algorithm structure learning |
| url | https://www.mdpi.com/2227-7390/13/9/1482 |
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