IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v108y2024i3d10.1007_s10182-023-00490-y.html
   My bibliography  Save this article

Bayesian generalized additive model selection including a fast variational option

Author

Listed:
  • Virginia X. He

    (University of Technology Sydney)

  • Matt P. Wand

    (University of Technology Sydney)

Abstract

We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be categorized as either zero, linear or non-linear. Employment of carefully tailored auxiliary variables results in Gibbsian Markov chain Monte Carlo schemes for practical implementation of the approach. In addition, mean field variational algorithms with closed form updates are obtained. Whilst not as accurate, this fast variational option enhances scalability to very large data sets. A package in the R language aids use in practice.

Suggested Citation

  • Virginia X. He & Matt P. Wand, 2024. "Bayesian generalized additive model selection including a fast variational option," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 639-668, September.
    • Handle: RePEc:spr:alstar:v:108:y:2024:i:3:d:10.1007_s10182-023-00490-y
    DOI: 10.1007/s10182-023-00490-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-023-00490-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-023-00490-y?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. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Scheipl, Fabian, 2011. "spikeSlabGAM: Bayesian Variable Selection, Model Choice and Regularization for Generalized Additive Mixed Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i14).
    3. Pradeep Ravikumar & John Lafferty & Han Liu & Larry Wasserman, 2009. "Sparse additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1009-1030, November.
    4. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    5. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    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. Luu, Tung Duy & Fadili, Jalal & Chesneau, Christophe, 2019. "PAC-Bayesian risk bounds for group-analysis sparse regression by exponential weighting," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 209-233.
    2. Niko Hauzenberger & Michael Pfarrhofer & Luca Rossini, 2020. "Sparse time-varying parameter VECMs with an application to modeling electricity prices," Papers 2011.04577, arXiv.org, revised Apr 2023.
    3. Jiang, Liewen & Bondell, Howard D. & Wang, Huixia Judy, 2014. "Interquantile shrinkage and variable selection in quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 208-219.
    4. Muhammad Jaffri Mohd Nasir & Ramzan Nazim Khan & Gopalan Nair & Darfiana Nur, 2024. "Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model," Statistical Papers, Springer, vol. 65(5), pages 2973-3006, July.
    5. Shizhe Chen & Ali Shojaie & Daniela M. Witten, 2017. "Network Reconstruction From High-Dimensional Ordinary Differential Equations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1697-1707, October.
    6. Siddhartha Nandy & Chae Young Lim & Tapabrata Maiti, 2017. "Additive model building for spatial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(3), pages 779-800, June.
    7. Yoshida, Takuma, 2018. "Semiparametric method for model structure discovery in additive regression models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 124-136.
    8. Adam N. Smith & Jim E. Griffin, 2023. "Shrinkage priors for high-dimensional demand estimation," Quantitative Marketing and Economics (QME), Springer, vol. 21(1), pages 95-146, March.
    9. Battauz, Michela & Vidoni, Paolo, 2022. "A likelihood-based boosting algorithm for factor analysis models with binary data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    10. Park, Jaewoo & Jin, Ick Hoon & Schweinberger, Michael, 2022. "Bayesian model selection for high-dimensional Ising models, with applications to educational data," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    11. Bai, Ray & Ghosh, Malay, 2018. "High-dimensional multivariate posterior consistency under global–local shrinkage priors," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 157-170.
    12. Yen, Tso-Jung & Yen, Yu-Min, 2016. "Structured variable selection via prior-induced hierarchical penalty functions," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 87-103.
    13. van Erp, Sara & Oberski, Daniel L. & Mulder, Joris, 2018. "Shrinkage priors for Bayesian penalized regression," OSF Preprints cg8fq, Center for Open Science.
    14. Fabian Scheipl & Thomas Kneib & Ludwig Fahrmeir, 2013. "Penalized likelihood and Bayesian function selection in regression models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 349-385, October.
    15. Feng, Zheng-Hui & Lin, Lu & Zhu, Ruo-Qing & Zhu, Li-Xing, 2018. "Nonparametric Variable Selection and Its Application to Additive Models," IRTG 1792 Discussion Papers 2018-002, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    16. Kshitij Khare & Malay Ghosh, 2022. "MCMC Convergence for Global-Local Shrinkage Priors," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 211-234, September.
    17. Naveen Naidu Narisetty, 2020. "Discussion," International Statistical Review, International Statistical Institute, vol. 88(2), pages 330-334, August.
    18. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2013. "A Survey of L1 Regression," International Statistical Review, International Statistical Institute, vol. 81(3), pages 361-387, December.
    19. M. Carvalho & S. Pereira & P. Pereira & P. Zea Bermudez, 2022. "An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 222-239, June.
    20. Yi Liu & Veronika Ročková & Yuexi Wang, 2021. "Variable selection with ABC Bayesian forests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 453-481, 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:spr:alstar:v:108:y:2024:i:3:d:10.1007_s10182-023-00490-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.