IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v137y2019icp67-91.html
   My bibliography  Save this article

Hierarchical estimation of parameters in Bayesian networks

Author

Listed:
  • Azzimonti, Laura
  • Corani, Giorgio
  • Zaffalon, Marco

Abstract

A novel approach for parameter estimation in Bayesian networks is presented. The main idea is to introduce a hyper-prior in the Multinomial–Dirichletmodel, traditionally used for conditional distribution estimation in Bayesian networks. The resulting hierarchical model jointly estimates different conditional distributions belonging to the same conditional probability table, thus borrowing statistical strength from each other. An analytical study of the dependence structure a priori induced by the hierarchical model is performed and an ad hoc variational algorithm for fast and accurate inference is derived. The proposed hierarchical model yields a major performance improvement in classification with Bayesian networks compared to traditional models. The proposed variational algorithm reduces by two orders of magnitude the computational time, with the same accuracy in parameter estimation, compared to traditional MCMC methods. Moreover, motivated by a real case study, the hierarchical model is applied to the estimation of Bayesian networks parameters by borrowing strength from related domains.

Suggested Citation

  • Azzimonti, Laura & Corani, Giorgio & Zaffalon, Marco, 2019. "Hierarchical estimation of parameters in Bayesian networks," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 67-91.
    • Handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:67-91
    DOI: 10.1016/j.csda.2019.02.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319300519
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.02.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Carpenter, Bob & Gelman, Andrew & Hoffman, Matthew D. & Lee, Daniel & Goodrich, Ben & Betancourt, Michael & Brubaker, Marcus & Guo, Jiqiang & Li, Peter & Riddell, Allen, 2017. "Stan: A Probabilistic Programming Language," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i01).
    2. Casella, George & Moreno, Elías, 2009. "Assessing Robustness of Intrinsic Tests of Independence in Two-Way Contingency Tables," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1261-1271.
    3. David M. Blei & Alp Kucukelbir & Jon D. McAuliffe, 2017. "Variational Inference: A Review for Statisticians," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 859-877, April.
    4. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    5. Grzegorczyk Marco & Husmeier Dirk, 2012. "A Non-Homogeneous Dynamic Bayesian Network with Sequentially Coupled Interaction Parameters for Applications in Systems and Synthetic Biology," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-62, July.
    6. Scutari, Marco, 2010. "Learning Bayesian Networks with the bnlearn R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i03).
    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. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    2. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    3. Linda S. L. Tan, 2021. "Use of model reparametrization to improve variational Bayes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(1), pages 30-57, February.
    4. Feihong Xia & Rabikar Chatterjee & Jerrold H. May, 2019. "Using Conditional Restricted Boltzmann Machines to Model Complex Consumer Shopping Patterns," Marketing Science, INFORMS, vol. 38(4), pages 711-727, July.
    5. Gael M. Martin & David T. Frazier & Christian P. Robert, 2021. "Approximating Bayes in the 21st Century," Monash Econometrics and Business Statistics Working Papers 24/21, Monash University, Department of Econometrics and Business Statistics.
    6. Bruno Jacobs & Dennis Fok & Bas Donkers, 2021. "Understanding Large-Scale Dynamic Purchase Behavior," Marketing Science, INFORMS, vol. 40(5), pages 844-870, September.
    7. Gael M. Martin & David T. Frazier & Worapree Maneesoonthorn & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2022. "Bayesian Forecasting in Economics and Finance: A Modern Review," Papers 2212.03471, arXiv.org, revised Jul 2023.
    8. Gael M. Martin & David T. Frazier & Christian P. Robert, 2022. "Computing Bayes: From Then `Til Now," Monash Econometrics and Business Statistics Working Papers 14/22, Monash University, Department of Econometrics and Business Statistics.
    9. Bansal, Prateek & Krueger, Rico & Bierlaire, Michel & Daziano, Ricardo A. & Rashidi, Taha H., 2020. "Bayesian estimation of mixed multinomial logit models: Advances and simulation-based evaluations," Transportation Research Part B: Methodological, Elsevier, vol. 131(C), pages 124-142.
    10. Zaid Tashman & Christoph Gorder & Sonali Parthasarathy & Mohamad M. Nasr-Azadani & Rachel Webre, 2020. "Anomaly Detection System for Water Networks in Northern Ethiopia Using Bayesian Inference," Sustainability, MDPI, vol. 12(7), pages 1-16, April.
    11. 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.
    12. Francis,David C. & Kubinec ,Robert, 2022. "Beyond Political Connections : A Measurement Model Approach to Estimating Firm-levelPolitical Influence in 41 Economies," Policy Research Working Paper Series 10119, The World Bank.
    13. Vuong, Quan-Hoang & La, Viet-Phuong, 2019. "The bayesvl R package. User guide v0.8.1," OSF Preprints w5dx6, Center for Open Science.
    14. Martinovici, A., 2019. "Revealing attention - how eye movements predict brand choice and moment of choice," Other publications TiSEM 7dca38a5-9f78-4aee-bd81-c, Tilburg University, School of Economics and Management.
    15. Yongping Bao & Ludwig Danwitz & Fabian Dvorak & Sebastian Fehrler & Lars Hornuf & Hsuan Yu Lin & Bettina von Helversen, 2022. "Similarity and Consistency in Algorithm-Guided Exploration," CESifo Working Paper Series 10188, CESifo.
    16. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," Papers 2012.14503, arXiv.org.
    17. 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.
    18. Redivo, Edoardo & Nguyen, Hien D. & Gupta, Mayetri, 2020. "Bayesian clustering of skewed and multimodal data using geometric skewed normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    19. van Kesteren Erik-Jan & Bergkamp Tom, 2023. "Bayesian analysis of Formula One race results: disentangling driver skill and constructor advantage," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 19(4), pages 273-293, December.
    20. Shen Liu & Hongyan Liu, 2021. "Tagging Items Automatically Based on Both Content Information and Browsing Behaviors," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 882-897, July.

    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:eee:csdana:v:137:y:2019:i:c:p:67-91. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.