IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2251-d1144540.html
   My bibliography  Save this article

An Improved Mixture Model of Gaussian Processes and Its Classification Expectation–Maximization Algorithm

Author

Listed:
  • Yurong Xie

    (School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, China
    These authors contributed equally to this work.)

  • Di Wu

    (School of Computer Science, Shaanxi Normal University, Xi’an 710119, China
    These authors contributed equally to this work.)

  • Zhe Qiang

    (School of Mathematics, Northwest University, Xi’an 710127, China)

Abstract

The mixture of experts (ME) model is effective for multimodal data in statistics and machine learning. To treat non-stationary probabilistic regression, the mixture of Gaussian processes (MGP) model has been proposed, but it may not perform well in some cases due to the limited ability of each Gaussian process (GP) expert. Although the mixture of Gaussian processes (MGP) and warped Gaussian process (WGP) models are dominant and effective for non-stationary probabilistic regression, they may not be able to handle general non-stationary probabilistic regression in practice. In this paper, we first propose the mixture of warped Gaussian processes (MWGP) model as well as its classification expectation–maximization (CEM) algorithm to address this problem. To overcome the local optimum of the CEM algorithm, we then propose the split and merge CEM (SMC EM) algorithm for MWGP. Experiments were done on synthetic and real-world datasets, which show that our proposed MWGP is more effective than the models used for comparison, and the SMCEM algorithm can solve the local optimum for MWGP.

Suggested Citation

  • Yurong Xie & Di Wu & Zhe Qiang, 2023. "An Improved Mixture Model of Gaussian Processes and Its Classification Expectation–Maximization Algorithm," Mathematics, MDPI, vol. 11(10), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2251-:d:1144540
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2251/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2251/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Brahim-Belhouari, Sofiane & Bermak, Amine, 2004. "Gaussian process for nonstationary time series prediction," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 705-712, November.
    2. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
    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. Adrian O’Hagan & Arthur White, 2019. "Improved model-based clustering performance using Bayesian initialization averaging," Computational Statistics, Springer, vol. 34(1), pages 201-231, March.
    2. François Bavaud, 2009. "Aggregation invariance in general clustering approaches," 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. 3(3), pages 205-225, December.
    3. Rasmus Lentz & Jean Marc Robin & Suphanit Piyapromdee, 2018. "On Worker and Firm Heterogeneity in Wages and Employment Mobility: Evidence from Danish Register Data," 2018 Meeting Papers 469, Society for Economic Dynamics.
    4. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    5. Mukhopadhyay, Subhadeep & Ghosh, Anil K., 2011. "Bayesian multiscale smoothing in supervised and semi-supervised kernel discriminant analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2344-2353, July.
    6. Grün, Bettina & Leisch, Friedrich, 2008. "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i04).
    7. Hornik, Kurt & Grün, Bettina, 2014. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i10).
    8. M. Vrac & L. Billard & E. Diday & A. Chédin, 2012. "Copula analysis of mixture models," Computational Statistics, Springer, vol. 27(3), pages 427-457, September.
    9. Bouveyron, C. & Girard, S. & Schmid, C., 2007. "High-dimensional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 502-519, September.
    10. repec:jss:jstsof:28:i04 is not listed on IDEAS
    11. Chehade, Abdallah & Savargaonkar, Mayuresh & Krivtsov, Vasiliy, 2022. "Conditional Gaussian mixture model for warranty claims forecasting," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    12. Nicolas Jouvin & Pierre Latouche & Charles Bouveyron & Guillaume Bataillon & Alain Livartowski, 2021. "Greedy clustering of count data through a mixture of multinomial PCA," Computational Statistics, Springer, vol. 36(1), pages 1-33, March.
    13. Andrawis, Robert R. & Atiya, Amir F. & El-Shishiny, Hisham, 2011. "Forecast combinations of computational intelligence and linear models for the NN5 time series forecasting competition," International Journal of Forecasting, Elsevier, vol. 27(3), pages 672-688, July.
    14. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
    15. Same, Allou & Ambroise, Christophe & Govaert, Gerard, 2006. "A classification EM algorithm for binned data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 466-480, November.
    16. Yves Grandvalet & Yoshua Bengio, 2004. "Learning from Partial Labels with Minimum Entropy," CIRANO Working Papers 2004s-28, CIRANO.
    17. Oscar Claveria & Enric Monte & Salvador Torra, 2016. "Modelling cross-dependencies between Spain’s regional tourism markets with an extension of the Gaussian process regression model," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(3), pages 341-357, August.
    18. Frei, Marco & Künsch, Hans R., 2013. "Mixture ensemble Kalman filters," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 127-138.
    19. Guan-Hua Huang & Su-Mei Wang & Chung-Chu Hsu, 2011. "Optimization-Based Model Fitting for Latent Class and Latent Profile Analyses," Psychometrika, Springer;The Psychometric Society, vol. 76(4), pages 584-611, October.
    20. Murphy, Thomas Brendan & Martin, Donal, 2003. "Mixtures of distance-based models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 645-655, January.
    21. Rasmus Lentz & Suphanit Piyapromdee & Jean-Marc Robin, 2022. "The Anatomy of Sorting - Evidence from Danish Data," SciencePo Working papers Main hal-03869383, HAL.

    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:gam:jmathe:v:11:y:2023:i:10:p:2251-:d:1144540. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.