IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i9p1482-d1646983.html
   My bibliography  Save this article

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

Author

Listed:
  • Ping-Feng Xu

    (Academy for Advanced Interdisciplinary Studies & Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, China
    Shanghai Zhangjiang Institute of Mathematics, Shanghai 201203, 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)

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.

Suggested Citation

  • Ping-Feng Xu & Shanyi Lin & Qian-Zhen Zheng & Man-Lai Tang, 2025. "Learning Gaussian Bayesian Network from Censored Data Subject to Limit of Detection by the Structural EM Algorithm," Mathematics, MDPI, vol. 13(9), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1482-:d:1646983
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/9/1482/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/9/1482/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. Sung Won Han & Gong Chen & Myun-Seok Cheon & Hua Zhong, 2016. "Estimation of Directed Acyclic Graphs Through Two-Stage Adaptive Lasso for Gene Network Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1004-1019, July.
    3. Fei Fu & Qing Zhou, 2013. "Learning Sparse Causal Gaussian Networks With Experimental Intervention: Regularization and Coordinate Descent," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 288-300, March.
    4. Daniela Marella & Paola Vicard, 2022. "Bayesian network structural learning from complex survey data: a resampling based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 981-1013, October.
    5. Scutari, Marco, 2010. "Learning Bayesian Networks with the bnlearn R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i03).
    6. Pesonen, Maiju & Pesonen, Henri & Nevalainen, Jaakko, 2015. "Covariance matrix estimation for left-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 13-25.
    7. Lee, Gyemin & Scott, Clayton, 2012. "EM algorithms for multivariate Gaussian mixture models with truncated and censored data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2816-2829.
    8. Jack Kuipers & Giusi Moffa, 2017. "Partition MCMC for Inference on Acyclic Digraphs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 282-299, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiao Guo & Hai Zhang, 2020. "Sparse directed acyclic graphs incorporating the covariates," Statistical Papers, Springer, vol. 61(5), pages 2119-2148, October.
    2. Leonelli, Manuele & Varando, Gherardo, 2024. "Robust learning of staged tree models: A case study in evaluating transport services," Socio-Economic Planning Sciences, Elsevier, vol. 95(C).
    3. Wang, Bingling & Zhou, Qing, 2021. "Causal network learning with non-invertible functional relationships," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    4. Zhang, Hongmei & Huang, Xianzheng & Han, Shengtong & Rezwan, Faisal I. & Karmaus, Wilfried & Arshad, Hasan & Holloway, John W., 2021. "Gaussian Bayesian network comparisons with graph ordering unknown," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    5. Jianyu Liu & Wei Sun & Yufeng Liu, 2019. "Joint skeleton estimation of multiple directed acyclic graphs for heterogeneous population," Biometrics, The International Biometric Society, vol. 75(1), pages 36-47, March.
    6. Prabal Das & D. A. Sachindra & Kironmala Chanda, 2022. "Machine Learning-Based Rainfall Forecasting with Multiple Non-Linear Feature Selection Algorithms," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(15), pages 6043-6071, December.
    7. Vuong, Quan-Hoang & La, Viet-Phuong, 2019. "The bayesvl R package. User guide v0.8.1," OSF Preprints w5dx6, Center for Open Science.
    8. Byron Botha & Rulof Burger & Kevin Kotzé & Neil Rankin & Daan Steenkamp, 2023. "Big data forecasting of South African inflation," Empirical Economics, Springer, vol. 65(1), pages 149-188, July.
    9. F. Cugnata & G. Perucca & S. Salini, 2017. "Bayesian networks and the assessment of universities' value added," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(10), pages 1785-1806, July.
    10. Frommlet, Florian & Ruhaltinger, Felix & Twaróg, Piotr & Bogdan, Małgorzata, 2012. "Modified versions of Bayesian Information Criterion for genome-wide association studies," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1038-1051.
    11. Zak-Szatkowska, Malgorzata & Bogdan, Malgorzata, 2011. "Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2908-2924, November.
    12. Roland R. Ramsahai, 2020. "Connecting actuarial judgment to probabilistic learning techniques with graph theory," Papers 2007.15475, arXiv.org.
    13. Tang, Kayu & Parsons, David J. & Jude, Simon, 2019. "Comparison of automatic and guided learning for Bayesian networks to analyse pipe failures in the water distribution system," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 24-36.
    14. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    15. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.
    16. Myriam Patricia Cifuentes & Clara Mercedes Suarez & Ricardo Cifuentes & Noel Malod-Dognin & Sam Windels & Jose Fernando Valderrama & Paul D. Juarez & R. Burciaga Valdez & Cynthia Colen & Charles Phill, 2022. "Big Data to Knowledge Analytics Reveals the Zika Virus Epidemic as Only One of Multiple Factors Contributing to a Year-Over-Year 28-Fold Increase in Microcephaly Incidence," IJERPH, MDPI, vol. 19(15), pages 1-21, July.
    17. Emre Demirkaya & Yang Feng & Pallavi Basu & Jinchi Lv, 2022. "Large-scale model selection in misspecified generalized linear models [Information theory and an extension of the maximum likelihood principle]," Biometrika, Biometrika Trust, vol. 109(1), pages 123-136.
    18. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    19. Lu Tang & Ling Zhou & Peter X. K. Song, 2019. "Fusion learning algorithm to combine partially heterogeneous Cox models," Computational Statistics, Springer, vol. 34(1), pages 395-414, March.
    20. Lian, Heng & Du, Pang & Li, YuanZhang & Liang, Hua, 2014. "Partially linear structure identification in generalized additive models with NP-dimensionality," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 197-208.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1482-:d:1646983. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.