IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v90y2022i3p563-591.html

Priors in Bayesian Deep Learning: A Review

Author

Listed:
  • Vincent Fortuin

Abstract

While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the importance of prior choices for Bayesian deep learning and present an overview of different priors that have been proposed for (deep) Gaussian processes, variational autoencoders and Bayesian neural networks. We also outline different methods of learning priors for these models from data. We hope to motivate practitioners in Bayesian deep learning to think more carefully about the prior specification for their models and to provide them with some inspiration in this regard.

Suggested Citation

  • Vincent Fortuin, 2022. "Priors in Bayesian Deep Learning: A Review," International Statistical Review, International Statistical Institute, vol. 90(3), pages 563-591, December.
    • Handle: RePEc:bla:istatr:v:90:y:2022:i:3:p:563-591
    DOI: 10.1111/insr.12502
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12502
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12502?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Andreas Kopf & Vincent Fortuin & Vignesh Ram Somnath & Manfred Claassen, 2021. "Mixture-of-Experts Variational Autoencoder for clustering and generating from similarity-based representations on single cell data," PLOS Computational Biology, Public Library of Science, vol. 17(6), pages 1-17, June.
    3. Simone Cerreia-Vioglio & Lars Peter Hansen & Fabio Maccheroni & Massimo Marinacci, 2020. "Making Decisions under Model Misspecification," Papers 2008.01071, arXiv.org, revised Aug 2022.
    4. Anindya Bhadra & Jyotishka Datta & Nicholas G. Polson & Brandon Willard, 2016. "Default Bayesian analysis with global-local shrinkage priors," Biometrika, Biometrika Trust, vol. 103(4), pages 955-969.
    5. repec:dau:papers:123456789/1908 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alsaadi, Fuad E. & Alharbi, Njud S. & Al-Barakati, Abdullah A., 2026. "Nonlinear dynamics and uncertainty-aware control of prosthetic systems using Bayesian Neural Networks and finite-time disturbance compensation," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    2. Mohseni-Gharyehsafa, Behnam & Hussain, Shahid & Fahy, Amy & De Rosa, Mattia & Pallonetto, Fabiano, 2025. "A hybrid Gaussian process-integrated deep learning model for retrofitted building energy optimization in smart city ecosystems," Applied Energy, Elsevier, vol. 388(C).

    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. Allassonnière, Stéphanie & Chevallier, Juliette, 2021. "A new class of stochastic EM algorithms. Escaping local maxima and handling intractable sampling," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    2. Riccardo Rastelli & Michael Fop, 2020. "A stochastic block model for interaction lengths," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 485-512, June.
    3. Deborah Gefang & Gary Koop & Aubrey Poon, 2019. "Variational Bayesian Inference in Large Vector Autoregressions with Hierarchical Shrinkage," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2019-07, Economic Statistics Centre of Excellence (ESCoE).
    4. Dayuan Wu & Ping Yan & You Guo & Han Zhou & Jian Chen, 2022. "A gear machining error prediction method based on adaptive Gaussian mixture regression considering stochastic disturbance," Journal of Intelligent Manufacturing, Springer, vol. 33(8), pages 2321-2339, December.
    5. Patrik Andersson & Mathias Lindholm, 2026. "Mortality Forecasting Using Variational Inference," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 45(3), pages 1069-1076, April.
    6. Lucas Kock & David T. Frazier & Michael Stanley Smith & David J. Nott, 2026. "Bayesian Modular Inference for Copula Models with Potentially Misspecified Marginals," Papers 2603.11457, arXiv.org, revised Apr 2026.
    7. 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.
    8. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    9. Mitra Kharabati & Morteza Amini & Mohammad Arashi, 2026. "Variational inference for sparse poisson regression," Computational Statistics, Springer, vol. 41(3), pages 1-50, April.
    10. Arnaldo Camuffo & Alfonso Gambardella & Andrea Pignataro, 2024. "Theory-Driven Strategic Management Decisions," Strategy Science, INFORMS, vol. 9(4), pages 382-396, December.
    11. Florian Mudekereza, 2025. "Robust Aggregation of Preferences," Papers 2504.07401, arXiv.org, revised Feb 2026.
    12. Bae, Youngkyoung & Ha, Seungwoong & Jeong, Hawoong, 2025. "Inferring the Langevin equation with uncertainty via Bayesian neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    13. Krueger, Rico & Rashidi, Taha H. & Vij, Akshay, 2020. "A Dirichlet process mixture model of discrete choice: Comparisons and a case study on preferences for shared automated vehicles," Journal of choice modelling, Elsevier, vol. 36(C).
    14. Qian, Yang & Ling, Haifeng & Meng, Xiangrui & Jiang, Yuanchun & Chai, Yidong & Liu, Yezheng, 2024. "Voice of the Professional: Acquiring competitive intelligence from large-scale professional generated contents," Journal of Business Research, Elsevier, vol. 180(C).
    15. Ankur Chavda & Joshua S. Gans & Scott Stern, 2024. "Theory-Based Entrepreneurial Search," Strategy Science, INFORMS, vol. 9(4), pages 397-415, December.
    16. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    17. Ying C. MacNab, 2018. "Rejoinder on: Some recent work on multivariate Gaussian Markov random fields," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 554-569, September.
    18. Gary Koop & Dimitris Korobilis, 2023. "Bayesian Dynamic Variable Selection In High Dimensions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 1047-1074, August.
    19. Chirag Nagpal & Robert E. Tillman & Prashant Reddy & Manuela Veloso, 2020. "Bayesian Consensus: Consensus Estimates from Miscalibrated Instruments under Heteroscedastic Noise," Papers 2004.06565, arXiv.org, revised Jan 2021.

    More about this item

    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:bla:istatr:v:90:y:2022:i:3:p:563-591. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    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.