IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v191y2022ics0047259x22000355.html
   My bibliography  Save this article

Bayesian joint inference for multiple directed acyclic graphs

Author

Listed:
  • Lee, Kyoungjae
  • Cao, Xuan

Abstract

In many applications, data often arise from multiple groups that may share similar characteristics. A joint estimation method that models several groups simultaneously can be more efficient than estimating parameters in each group separately. We focus on unraveling the dependence structures of data based on directed acyclic graphs with a known parent ordering and propose a Bayesian joint inference method for multiple graphs. To encourage similar dependence structures across all groups, a Markov random field prior is adopted. We establish joint selection consistency and posterior convergence rates of the fractional posterior in high dimensions. This is the first theoretically supported Bayesian method for joint estimation of multiple directed acyclic graphs. The performance of the proposed method is demonstrated using simulation studies, and it is shown that our joint inference outperforms other competitors. We apply our method to an fMRI data for simultaneously inferring multiple brain functional networks.

Suggested Citation

  • Lee, Kyoungjae & Cao, Xuan, 2022. "Bayesian joint inference for multiple directed acyclic graphs," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:jmvana:v:191:y:2022:i:c:s0047259x22000355
    DOI: 10.1016/j.jmva.2022.105003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X22000355
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2022.105003?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. 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. Christine B. Peterson & Nathan Osborne & Francesco C. Stingo & Pierrick Bourgeat & James D. Doecke & Marina Vannucci, 2020. "Bayesian modeling of multiple structural connectivity networks during the progression of Alzheimer's disease," Biometrics, The International Biometric Society, vol. 76(4), pages 1120-1132, December.
    3. Yang Ni & Peter Müller & Yitan Zhu & Yuan Ji, 2018. "Heterogeneous reciprocal graphical models," Biometrics, The International Biometric Society, vol. 74(2), pages 606-615, June.
    4. Ali Shojaie & George Michailidis, 2010. "Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs," Biometrika, Biometrika Trust, vol. 97(3), pages 519-538.
    5. Patrick Danaher & Pei Wang & Daniela M. Witten, 2014. "The joint graphical lasso for inverse covariance estimation across multiple classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 373-397, March.
    6. Banerjee, Sayantan & Ghosal, Subhashis, 2015. "Bayesian structure learning in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 147-162.
    7. 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.
    8. Christine Peterson & Francesco C. Stingo & Marina Vannucci, 2015. "Bayesian Inference of Multiple Gaussian Graphical Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 159-174, March.
    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. Yang Ni & Veerabhadran Baladandayuthapani & Marina Vannucci & Francesco C. Stingo, 2022. "Bayesian graphical models for modern biological applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 197-225, June.
    2. 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).
    3. Lin Zhang & Andrew DiLernia & Karina Quevedo & Jazmin Camchong & Kelvin Lim & Wei Pan, 2021. "A random covariance model for bi‐level graphical modeling with application to resting‐state fMRI data," Biometrics, The International Biometric Society, vol. 77(4), pages 1385-1396, December.
    4. Mehran Aflakparast & Mathisca de Gunst & Wessel van Wieringen, 2020. "Analysis of Twitter data with the Bayesian fused graphical lasso," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-28, July.
    5. Wessel N. van Wieringen & Carel F. W. Peeters & Renee X. de Menezes & Mark A. van de Wiel, 2018. "Testing for pathway (in)activation by using Gaussian graphical models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1419-1436, November.
    6. Anindya Bhadra, 2022. "Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(2), pages 235-239, June.
    7. Yang Ni & Peter Müller & Yitan Zhu & Yuan Ji, 2018. "Heterogeneous reciprocal graphical models," Biometrics, The International Biometric Society, vol. 74(2), pages 606-615, June.
    8. Christine B. Peterson & Nathan Osborne & Francesco C. Stingo & Pierrick Bourgeat & James D. Doecke & Marina Vannucci, 2020. "Bayesian modeling of multiple structural connectivity networks during the progression of Alzheimer's disease," Biometrics, The International Biometric Society, vol. 76(4), pages 1120-1132, December.
    9. Daniel Felix Ahelegbey & Monica Billio & Roberto Casarin, 2016. "Sparse Graphical Vector Autoregression: A Bayesian Approach," Annals of Economics and Statistics, GENES, issue 123-124, pages 333-361.
    10. Yang Ni & Francesco C. Stingo & Veerabhadran Baladandayuthapani, 2015. "Bayesian nonlinear model selection for gene regulatory networks," Biometrics, The International Biometric Society, vol. 71(3), pages 585-595, September.
    11. Zhixiang Lin & Tao Wang & Can Yang & Hongyu Zhao, 2017. "On joint estimation of Gaussian graphical models for spatial and temporal data," Biometrics, The International Biometric Society, vol. 73(3), pages 769-779, September.
    12. Cao, Xuan & Khare, Kshitij & Ghosh, Malay, 2020. "Consistent Bayesian sparsity selection for high-dimensional Gaussian DAG models with multiplicative and beta-mixture priors," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    13. 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.
    14. Elin Shaddox & Francesco C. Stingo & Christine B. Peterson & Sean Jacobson & Charmion Cruickshank-Quinn & Katerina Kechris & Russell Bowler & Marina Vannucci, 2018. "A Bayesian Approach for Learning Gene Networks Underlying Disease Severity in COPD," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(1), pages 59-85, April.
    15. Marco Molinari & Andrea Cremaschi & Maria De Iorio & Nishi Chaturvedi & Alun D. Hughes & Therese Tillin, 2022. "Bayesian nonparametric modelling of multiple graphs with an application to ethnic metabolic differences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1181-1204, November.
    16. Conte, Federica & Costantini, Giulio & Rinaldi, Luca & Gerosa, Tiziano & Girelli, Luisa, 2020. "Intellect is not that expensive: differential association of cultural and socio-economic factors with crystallized intelligence in a sample of Italian adolescents," Intelligence, Elsevier, vol. 81(C).
    17. Junghi Kim & Kim‐Anh Do & Min Jin Ha & Christine B. Peterson, 2019. "Bayesian inference of hub nodes across multiple networks," Biometrics, The International Biometric Society, vol. 75(1), pages 172-182, March.
    18. Meichen Dong & Yiping He & Yuchao Jiang & Fei Zou, 2023. "Joint gene network construction by single‐cell RNA sequencing data," Biometrics, The International Biometric Society, vol. 79(2), pages 915-925, June.
    19. Atchadé, Yves F., 2019. "Quasi-Bayesian estimation of large Gaussian graphical models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 656-671.
    20. Beatrice Franzolini & Alexandros Beskos & Maria De Iorio & Warrick Poklewski Koziell & Karolina Grzeszkiewicz, 2022. "Change point detection in dynamic Gaussian graphical models: the impact of COVID-19 pandemic on the US stock market," Papers 2208.00952, arXiv.org, revised May 2023.

    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:191:y:2022:i:c:s0047259x22000355. 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.