IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v38y2023i4d10.1007_s00180-022-01300-w.html
   My bibliography  Save this article

Probabilistic learning constrained by realizations using a weak formulation of Fourier transform of probability measures

Author

Listed:
  • Christian Soize

    (Université Gustave Eiffel)

Abstract

This paper deals with the taking into account a given target set of realizations as constraints in the Kullback–Leibler divergence minimum principle (KLDMP). We present a novel probabilistic learning algorithm that makes it possible to use the KLDMP when the constraints are not defined by a target set of statistical moments for the quantity of interest (QoI) of an uncertain/stochastic computational model, but are defined by a target set of realizations for the QoI for which the statistical moments associated with these realizations are not or cannot be estimated. The method consists in defining a functional constraint, as the equality of the Fourier transforms of the posterior probability measure and the target probability measure, and in constructing a finite representation of the weak formulation of this functional constraint. The proposed approach allows for estimating the posterior probability measure of the QoI (unsupervised case) or of the posterior joint probability measure of the QoI with the control parameter (supervised case). The existence and the uniqueness of the posterior probability measure is analyzed for the two cases. The numerical aspects are detailed in order to facilitate the implementation of the proposed method. The presented application in high dimension demonstrates the efficiency and the robustness of the proposed algorithm.

Suggested Citation

  • Christian Soize, 2023. "Probabilistic learning constrained by realizations using a weak formulation of Fourier transform of probability measures," Computational Statistics, Springer, vol. 38(4), pages 1879-1925, December.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:4:d:10.1007_s00180-022-01300-w
    DOI: 10.1007/s00180-022-01300-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-022-01300-w
    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/s00180-022-01300-w?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. Perrin, G. & Soize, C. & Ouhbi, N., 2018. "Data-driven kernel representations for sampling with an unknown block dependence structure under correlation constraints," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 139-154.
    2. Nicolas Depraetere & Martina Vandebroek, 2017. "A comparison of variational approximations for fast inference in mixed logit models," Computational Statistics, Springer, vol. 32(1), pages 93-125, March.
    3. repec:dau:papers:123456789/5724 is not listed on IDEAS
    4. Yuan Shen & Dan Cornford & Manfred Opper & Cedric Archambeau, 2012. "Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions," Computational Statistics, Springer, vol. 27(1), pages 149-176, March.
    5. Rajiv Sambasivan & Sourish Das & Sujit K. Sahu, 2020. "A Bayesian perspective of statistical machine learning for big data," Computational Statistics, Springer, vol. 35(3), pages 893-930, September.
    6. Mark Girolami & Ben Calderhead, 2011. "Riemann manifold Langevin and Hamiltonian Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 123-214, March.
    7. Guillaume Perrin & Christian Soize, 2020. "Adaptive method for indirect identification of the statistical properties of random fields in a Bayesian framework," Computational Statistics, Springer, vol. 35(1), pages 111-133, 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. Ranjan, Rakesh & Sen, Rijji & Upadhyay, Satyanshu K., 2021. "Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    2. Ioannis Bournakis & Mike Tsionas, 2024. "A Non‐parametric Estimation of Productivity with Idiosyncratic and Aggregate Shocks: The Role of Research and Development (R&D) and Corporate Tax," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(3), pages 641-671, June.
    3. Chen, Zhongfei & Wanke, Peter & Tsionas, Mike G., 2018. "Assessing the strategic fit of potential M&As in Chinese banking: A novel Bayesian stochastic frontier approach," Economic Modelling, Elsevier, vol. 73(C), pages 254-263.
    4. Atkinson, Scott E. & Tsionas, Mike G., 2021. "Generalized estimation of productivity with multiple bad outputs: The importance of materials balance constraints," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1165-1186.
    5. Tsionas, Mike G. & Malikov, Emir & Kumbhakar, Subal C., 2020. "Endogenous dynamic efficiency in the intertemporal optimization models of firm behavior," European Journal of Operational Research, Elsevier, vol. 284(1), pages 313-324.
    6. Raphaël Douady & Shohruh Miryusupov, 2017. "Hamiltonian Flow Simulation of Rare Events," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01581894, HAL.
    7. Caroline Khan & Mike G. Tsionas, 2021. "Constraints in models of production and cost via slack-based measures," Empirical Economics, Springer, vol. 61(6), pages 3347-3374, December.
    8. Topaloglou, Nikolas & Tsionas, Mike G., 2020. "Stochastic dominance tests," Journal of Economic Dynamics and Control, Elsevier, vol. 112(C).
    9. Jia Liu & John M. Maheu & Yong Song, 2024. "Identification and forecasting of bull and bear markets using multivariate returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 723-745, August.
    10. Dimitrakopoulos, Stefanos & Tsionas, Mike, 2019. "Ordinal-response GARCH models for transaction data: A forecasting exercise," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1273-1287.
    11. 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).
    12. Kutlu, Levent & Mamatzakis, Emmanuel & Tsionas, Mike G., 2022. "A principal–agent approach for estimating firm efficiency: Revealing bank managerial behavior," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 79(C).
    13. De Silva, Dakshina G. & Hubbard, Timothy P. & Schiller, Anita R. & Tsionas, Mike G., 2023. "Estimating outcomes in the presence of endogeneity and measurement error with an application to R&D," The Quarterly Review of Economics and Finance, Elsevier, vol. 88(C), pages 278-294.
    14. 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.
    15. Vanhatalo, Jarno & Veneranta, Lari & Hudd, Richard, 2012. "Species distribution modeling with Gaussian processes: A case study with the youngest stages of sea spawning whitefish (Coregonus lavaretus L. s.l.) larvae," Ecological Modelling, Elsevier, vol. 228(C), pages 49-58.
    16. Stephen G. Hall & Heather D. Gibson & G. S. Tavlas & Mike G. Tsionas, 2020. "A Monte Carlo Study of Time Varying Coefficient (TVC) Estimation," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 115-130, June.
    17. Rubing Liang & Binbin Qin & Qiang Xia, 2024. "Bayesian Inference for Mixed Gaussian GARCH-Type Model by Hamiltonian Monte Carlo Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 193-220, January.
    18. Will Penny & Biswa Sengupta, 2016. "Annealed Importance Sampling for Neural Mass Models," PLOS Computational Biology, Public Library of Science, vol. 12(3), pages 1-25, March.
    19. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2016. "The good, the bad and the technology: Endogeneity in environmental production models," Journal of Econometrics, Elsevier, vol. 190(2), pages 315-327.
    20. Tore Selland Kleppe, 2016. "Adaptive Step Size Selection for Hessian-Based Manifold Langevin Samplers," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 788-805, 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:spr:compst:v:38:y:2023:i:4:d:10.1007_s00180-022-01300-w. 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.