IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v202y2025ics0167947324001397.html
   My bibliography  Save this article

A variational inference framework for inverse problems

Author

Listed:
  • Maestrini, Luca
  • Aykroyd, Robert G.
  • Wand, Matt P.

Abstract

A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model fitting times. The message passing and factor graph fragment approach to variational Bayes that is also described facilitates streamlined implementation of approximate inference algorithms and allows for supple inclusion of numerous response distributions and penalizations into the inverse problem model. Models for one- and two-dimensional response variables are examined and an infrastructure is laid down where efficient algorithm updates based on nullifying weak interactions between variables can also be derived for inverse problems in higher dimensions. An image processing application and a simulation exercise motivated by biomedical problems reveal the computational advantage offered by efficient implementation of variational Bayes over Markov chain Monte Carlo.

Suggested Citation

  • Maestrini, Luca & Aykroyd, Robert G. & Wand, Matt P., 2025. "A variational inference framework for inverse problems," Computational Statistics & Data Analysis, Elsevier, vol. 202(C).
    • Handle: RePEc:eee:csdana:v:202:y:2025:i:c:s0167947324001397
    DOI: 10.1016/j.csda.2024.108055
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324001397
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.108055?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. G. T. Allum & R. G. Aykroyd & J. G. B. Haigh, 1999. "Empirical Bayes estimation for archaeological stratigraphy," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 1-14.
    3. Furrer, Reinhard & Sain, Stephan R., 2010. "spam: A Sparse Matrix R Package with Emphasis on MCMC Methods for Gaussian Markov Random Fields," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 36(i10).
    4. M. P. Wand, 2017. "Fast Approximate Inference for Arbitrarily Large Semiparametric Regression Models via Message Passing," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 137-168, January.
    5. F. S. Nathoo & A. Babul & A. Moiseev & N. Virji-Babul & M. F. Beg, 2014. "A variational Bayes spatiotemporal model for electromagnetic brain mapping," Biometrics, The International Biometric Society, vol. 70(1), pages 132-143, 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. Mauro Bernardi & Daniele Bianchi & Nicolas Bianco, 2022. "Variational inference for large Bayesian vector autoregressions," Papers 2202.12644, arXiv.org, revised Jun 2023.
    2. Roman Flury & Reinhard Furrer, 2021. "Discussion on Competition for Spatial Statistics for Large Datasets," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(4), pages 599-603, December.
    3. Tamal Ghosh & Malay Ghosh & Jerry J. Maples & Xueying Tang, 2022. "Multivariate Global-Local Priors for Small Area Estimation," Stats, MDPI, vol. 5(3), pages 1-16, July.
    4. Martin Feldkircher & Florian Huber & Gary Koop & Michael Pfarrhofer, 2022. "APPROXIMATE BAYESIAN INFERENCE AND FORECASTING IN HUGE‐DIMENSIONAL MULTICOUNTRY VARs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1625-1658, November.
    5. Davies, Tilman M. & Bryant, David, 2013. "On Circulant Embedding for Gaussian Random Fields in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i09).
    6. Phella, Anthoulla & Gabriel, Vasco J. & Martins, Luis F., 2024. "Predicting tail risks and the evolution of temperatures," Energy Economics, Elsevier, vol. 131(C).
    7. Loaiza-Maya, Rubén & Smith, Michael Stanley & Nott, David J. & Danaher, Peter J., 2022. "Fast and accurate variational inference for models with many latent variables," Journal of Econometrics, Elsevier, vol. 230(2), pages 339-362.
    8. Alla A. Petukhina & Raphael C. G. Reule & Wolfgang Karl Härdle, 2021. "Rise of the machines? Intraday high-frequency trading patterns of cryptocurrencies," The European Journal of Finance, Taylor & Francis Journals, vol. 27(1-2), pages 8-30, January.
    9. Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
    10. Martin Guth, 2022. "Predicting Default Probabilities for Stress Tests: A Comparison of Models," Papers 2202.03110, arXiv.org.
    11. Dimitris Korobilis, 2021. "High-Dimensional Macroeconomic Forecasting Using Message Passing Algorithms," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 493-504, March.
    12. 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.
    13. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.
    14. Todd E. Clark & Florian Huber & Gary Koop & Massimiliano Marcellino & Michael Pfarrhofer, 2023. "Tail Forecasting With Multivariate Bayesian Additive Regression Trees," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(3), pages 979-1022, August.
    15. Chan, Joshua C.C., 2021. "Minnesota-type adaptive hierarchical priors for large Bayesian VARs," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1212-1226.
    16. Ander Wilson & Brian J. Reich, 2014. "Confounder selection via penalized credible regions," Biometrics, The International Biometric Society, vol. 70(4), pages 852-861, December.
    17. Luca Barbaglia & Lorenzo Frattarolo & Niko Hauzenberger & Dominik Hirschbuehl & Florian Huber & Luca Onorante & Michael Pfarrhofer & Luca Tiozzo Pezzoli, 2024. "Nowcasting economic activity in European regions using a mixed-frequency dynamic factor model," Papers 2401.10054, arXiv.org.
    18. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2021. "Economic Predictions With Big Data: The Illusion of Sparsity," Econometrica, Econometric Society, vol. 89(5), pages 2409-2437, September.
    19. Lukas Berend & Jan Pruser, 2024. "The Transmission of Monetary Policy via Common Cycles in the Euro Area," Papers 2410.05741, arXiv.org, revised Nov 2024.
    20. 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.

    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:202:y:2025:i:c:s0167947324001397. 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.