IDEAS home Printed from https://ideas.repec.org/a/spr/jstada/v8y2021i1d10.1186_s40488-021-00125-0.html
   My bibliography  Save this article

Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models

Author

Listed:
  • Hien Duy Nguyen

    (La Trobe University)

  • TrungTin Nguyen

    (Normandie Univ, UNICAEN, CNRS, LMNO)

  • Faicel Chamroukhi

    (Normandie Univ, UNICAEN, CNRS, LMNO)

  • Geoffrey John McLachlan

    (School of Mathematics and Physics, University of Queensland)

Abstract

Mixture of experts (MoE) models are widely applied for conditional probability density estimation problems. We demonstrate the richness of the class of MoE models by proving denseness results in Lebesgue spaces, when inputs and outputs variables are both compactly supported. We further prove an almost uniform convergence result when the input is univariate. Auxiliary lemmas are proved regarding the richness of the soft-max gating function class, and their relationships to the class of Gaussian gating functions.

Suggested Citation

  • Hien Duy Nguyen & TrungTin Nguyen & Faicel Chamroukhi & Geoffrey John McLachlan, 2021. "Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.
    • Handle: RePEc:spr:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00125-0
    DOI: 10.1186/s40488-021-00125-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1186/s40488-021-00125-0
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1186/s40488-021-00125-0?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. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    2. Perthame, Emeline & Forbes, Florence & Deleforge, Antoine, 2018. "Inverse regression approach to robust nonlinear high-to-low dimensional mapping," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 1-14.
    3. Norets, Andriy & Pelenis, Justinas, 2014. "Posterior Consistency In Conditional Density Estimation By Covariate Dependent Mixtures," Econometric Theory, Cambridge University Press, vol. 30(3), pages 606-646, June.
    4. Ingrassia, Salvatore & Minotti, Simona C. & Punzo, Antonio, 2014. "Model-based clustering via linear cluster-weighted models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 159-182.
    5. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
    6. Kalliovirta, Leena & Meitz, Mika & Saikkonen, Pentti, 2016. "Gaussian mixture vector autoregression," Journal of Econometrics, Elsevier, vol. 192(2), pages 485-498.
    7. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
    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. Corsini, Noemi & Viroli, Cinzia, 2022. "Dealing with overdispersion in multivariate count data," Computational Statistics & Data Analysis, Elsevier, vol. 170(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. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    2. Paolo Berta & Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini, 2016. "Multilevel cluster-weighted models for the evaluation of hospitals," METRON, Springer;Sapienza Università di Roma, vol. 74(3), pages 275-292, December.
    3. Diani, Cecilia & Galimberti, Giuliano & Soffritti, Gabriele, 2022. "Multivariate cluster-weighted models based on seemingly unrelated linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    4. Salvatore Ingrassia & Antonio Punzo, 2020. "Cluster Validation for Mixtures of Regressions via the Total Sum of Squares Decomposition," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 526-547, July.
    5. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
    6. Gabriele Soffritti, 2021. "Estimating the Covariance Matrix of the Maximum Likelihood Estimator Under Linear Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 594-625, October.
    7. Norets, Andriy, 2015. "Bayesian regression with nonparametric heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 409-419.
    8. Yang, Yu-Chen & Lin, Tsung-I & Castro, Luis M. & Wang, Wan-Lun, 2020. "Extending finite mixtures of t linear mixed-effects models with concomitant covariates," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    9. Michael P. B. Gallaugher & Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2022. "Multivariate cluster weighted models using skewed distributions," 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. 16(1), pages 93-124, March.
    10. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    11. Utkarsh J. Dang & Antonio Punzo & Paul D. McNicholas & Salvatore Ingrassia & Ryan P. Browne, 2017. "Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 4-34, April.
    12. Hien Nguyen & Geoffrey McLachlan, 2015. "Maximum likelihood estimation of Gaussian mixture models without matrix operations," 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. 9(4), pages 371-394, December.
    13. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    14. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, March.
    15. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    16. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    17. Sanjeena Subedi & Antonio Punzo & Salvatore Ingrassia & Paul McNicholas, 2015. "Cluster-weighted $$t$$ t -factor analyzers for robust model-based clustering and dimension reduction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 623-649, November.
    18. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 85-113, April.
    19. Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    20. Sangkon Oh & Byungtae Seo, 2023. "Merging Components in Linear Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 25-51, April.

    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:jstada:v:8:y:2021:i:1:d:10.1186_s40488-021-00125-0. 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.