IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v203y2024ics0047259x24000307.html
   My bibliography  Save this article

Bayesian inference of graph-based dependencies from mixed-type data

Author

Listed:
  • Galimberti, Chiara
  • Peluso, Stefano
  • Castelletti, Federico

Abstract

Mixed data comprise measurements of different types, with both categorical and continuous variables, and can be found in various areas, such as in life science or industrial processes. Inferring conditional independencies from the data is crucial to understand how these variables relate to each other. To this end, graphical models provide an effective framework, which adopts a graph-based representation of the joint distribution to encode such dependence relations. This framework has been extensively studied in the Gaussian and categorical settings separately; on the other hand, the literature addressing this problem in presence of mixed data is still narrow. We propose a Bayesian model for the analysis of mixed data based on the notion of Conditional Gaussian (CG) distribution. Our method is based on a canonical parameterization of the CG distribution, which allows for posterior inference of parameters indexing the (marginal) distributions of continuous and categorical variables, as well as expressing the interactions between the two types of variables. We derive the limiting Gaussian distributions, centered on the correct unknown value and with vanishing variance, for the Bayesian estimators of the canonical parameters expressing continuous, discrete and mixed interactions. In addition, we implement the proposed method for structure learning purposes, namely to infer the underlying graph of conditional independencies. When compared to alternative frequentist methods, our approach shows favorable results both in a simulation setting and in real-data applications, besides allowing for a coherent uncertainty quantification around parameter estimates.

Suggested Citation

  • Galimberti, Chiara & Peluso, Stefano & Castelletti, Federico, 2024. "Bayesian inference of graph-based dependencies from mixed-type data," Journal of Multivariate Analysis, Elsevier, vol. 203(C).
  • Handle: RePEc:eee:jmvana:v:203:y:2024:i:c:s0047259x24000307
    DOI: 10.1016/j.jmva.2024.105323
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X24000307
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2024.105323?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. Fellinghauer, Bernd & Bühlmann, Peter & Ryffel, Martin & von Rhein, Michael & Reinhardt, Jan D., 2013. "Stable graphical model estimation with Random Forests for discrete, continuous, and mixed variables," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 132-152.
    2. Anindya Bhadra & Bani K. Mallick, 2013. "Joint High-Dimensional Bayesian Variable and Covariance Selection with an Application to eQTL Analysis," Biometrics, The International Biometric Society, vol. 69(2), pages 447-457, June.
    3. Castelletti, Federico & Peluso, Stefano, 2021. "Equivalence class selection of categorical graphical models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    4. Shizhe Chen & Daniela M. Witten & Ali Shojaie, 2015. "Selection and estimation for mixed graphical models," Biometrika, Biometrika Trust, vol. 102(1), pages 47-64.
    5. Dasgupta, Tirthankar & Ma, Christopher & Joseph, V. Roshan & Wang, Z.L. & Wu, C. F. Jeff, 2008. "Statistical Modeling and Analysis for Robust Synthesis of Nanostructures," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 594-603, June.
    6. Abdolreza Mohammadi & Fentaw Abegaz & Edwin Heuvel & Ernst C. Wit, 2017. "Bayesian modelling of Dupuytren disease by using Gaussian copula graphical models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(3), pages 629-645, April.
    7. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
    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. Anindya Bhadra & Arvind Rao & Veerabhadran Baladandayuthapani, 2018. "Inferring network structure in non†normal and mixed discrete†continuous genomic data," Biometrics, The International Biometric Society, vol. 74(1), pages 185-195, March.
    2. Jianqing Fan & Han Liu & Yang Ning & Hui Zou, 2017. "High dimensional semiparametric latent graphical model for mixed data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 405-421, March.
    3. Hengtao Zhang & Guosheng Yin, 2021. "Response‐adaptive rerandomization," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(5), pages 1281-1298, November.
    4. Andrew Gelman & Daniel Lee & Jiqiang Guo, 2015. "Stan," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 530-543, October.
    5. Zuoxian Gan & Tao Feng & Min Yang, 2018. "Exploring the Effects of Car Ownership and Commuting on Subjective Well-Being: A Nationwide Questionnaire Study," Sustainability, MDPI, vol. 11(1), pages 1-20, December.
    6. Paci, Lucia & Consonni, Guido, 2020. "Structural learning of contemporaneous dependencies in graphical VAR models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    7. Antonio Parisi & B. Liseo, 2018. "Objective Bayesian analysis for the multivariate skew-t model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 277-295, June.
    8. Bakar, Khandoker Shuvo & Sahu, Sujit K., 2015. "spTimer: Spatio-Temporal Bayesian Modeling Using R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 63(i15).
    9. Baştürk, Nalan & Grassi, Stefano & Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2017. "The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i01).
    10. van Wieringen, Wessel N. & Stam, Koen A. & Peeters, Carel F.W. & van de Wiel, Mark A., 2020. "Updating of the Gaussian graphical model through targeted penalized estimation," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    11. White, Robin R. & Brady, Michael, 2014. "Can consumers’ willingness to pay incentivize adoption of environmental impact reducing technologies in meat animal production?," Food Policy, Elsevier, vol. 49(P1), pages 41-49.
    12. Kim, Kyongwon, 2022. "On principal graphical models with application to gene network," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    13. Xin Fang & Bo Fang & Chunfang Wang & Tian Xia & Matteo Bottai & Fang Fang & Yang Cao, 2019. "Comparison of Frequentist and Bayesian Generalized Additive Models for Assessing the Association between Daily Exposure to Fine Particles and Respiratory Mortality: A Simulation Study," IJERPH, MDPI, vol. 16(5), pages 1-20, March.
    14. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    15. Schaarschmidt, Frank & Gerhard, Daniel & Vogel, Charlotte, 2017. "Simultaneous confidence intervals for comparisons of several multinomial samples," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 65-76.
    16. Eijffinger, Sylvester & Mahieu, Ronald & Raes, Louis, 2018. "Inferring hawks and doves from voting records," European Journal of Political Economy, Elsevier, vol. 51(C), pages 107-120.
    17. Martin Hernani Merino & Enver Gerald Tarazona Vargas & Antonieta Hamann Pastorino & José Afonso Mazzon, 2014. "Validation of Sustainable Development Practices Scale Using the Bayesian Approach to Item Response Theory," Tržište/Market, Faculty of Economics and Business, University of Zagreb, vol. 26(2), pages 147-162.
    18. Tâmara Rebecca A. de Oliveira & Moysés Nascimento & Paulo R. Santos & Kleyton Danilo S. Costa & Thalyson V. Lima & Gabriela Karoline Michelon & Luis Claudio de Faria & Antonio F. Costa & José Wilso, 2024. "Bayesian Perspective in the Selection of Bean Genotypes," Journal of Agricultural Science, Canadian Center of Science and Education, vol. 12(9), pages 173-173, April.
    19. repec:jss:jstsof:39:i12 is not listed on IDEAS
    20. Emmanuel Mensaklo & Chukiat Chaiboonsri & Kanchana Chokethaworn & Songsak Sriboonchitta, 2023. "Comparing Classical and Bayesian Panel Kink Regression Frameworks in Estimating the Impact of Economic Freedom on Economic Growth," Economies, MDPI, vol. 11(10), pages 1-24, October.
    21. Daniel W. Hill Jr., 2016. "Avoiding Obligation," Journal of Conflict Resolution, Peace Science Society (International), vol. 60(6), pages 1129-1158, September.

    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:jmvana:v:203:y:2024:i:c:s0047259x24000307. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.