IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i12p4122-4137.html
   My bibliography  Save this article

Acceleration of the EM algorithm: P-EM versus epsilon algorithm

Author

Listed:
  • Berlinet, A.F.
  • Roland, Ch.

Abstract

Among recent methods designed for accelerating the EM algorithm without any modification in the structure of EM or in the statistical model, the parabolic acceleration (P-EM) has proved its efficiency. It does not involve any computation of gradient or hessian matrix and can be used as an additional software component of any fixed point algorithm maximizing some objective function. The vector epsilon algorithm was introduced to reach the same goals. Through geometric considerations, the relationships between the outputs of an improved version of P-EM and those of the vector epsilon algorithm are established. This sheds some light on their different behaviours and explains why the parabolic acceleration of EM outperforms its competitor in most numerical experiments. A detailed analysis of its trajectories in a variety of real or simulated data shows the ability of P-EM to choose the most efficient paths to the global maximum of the likelihood.

Suggested Citation

  • Berlinet, A.F. & Roland, Ch., 2012. "Acceleration of the EM algorithm: P-EM versus epsilon algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4122-4137.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:4122-4137
    DOI: 10.1016/j.csda.2012.03.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312001314
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.03.005?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. Mingfeng Wang & Masahiro Kuroda & Michio Sakakihara & Zhi Geng, 2008. "Acceleration of the EM algorithm using the vector epsilon algorithm," Computational Statistics, Springer, vol. 23(3), pages 469-486, July.
    2. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    3. Kuroda, Masahiro & Sakakihara, Michio, 2006. "Accelerating the convergence of the EM algorithm using the vector [epsilon] algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1549-1561, December.
    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. Chen, Shu-Chuan (Grace) & Lindsay, Bruce, 2014. "Improving mixture tree construction using better EM algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 17-25.
    2. Ippel, L. & Kaptein, M.C. & Vermunt, J.K., 2016. "Estimating random-intercept models on data streams," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 169-182.
    3. Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    4. Jurgen A. Doornik, 2018. "Accelerated Estimation of Switching Algorithms: The Cointegrated VAR Model and Other Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 283-300, June.

    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. Masahiro Kuroda & Zhi Geng & Michio Sakakihara, 2015. "Improving the vector $$\varepsilon $$ ε acceleration for the EM algorithm using a re-starting procedure," Computational Statistics, Springer, vol. 30(4), pages 1051-1077, December.
    2. Tian, Guo-Liang & Tang, Man-Lai & Liu, Chunling, 2012. "Accelerating the quadratic lower-bound algorithm via optimizing the shrinkage parameter," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 255-265.
    3. Kuroda, Masahiro & Mori, Yuichi & Iizuka, Masaya & Sakakihara, Michio, 2011. "Acceleration of the alternating least squares algorithm for principal components analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 143-153, January.
    4. Saâdaoui, Foued, 2010. "Acceleration of the EM algorithm via extrapolation methods: Review, comparison and new methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 750-766, March.
    5. Saâdaoui, Foued, 2023. "Randomized extrapolation for accelerating EM-type fixed-point algorithms," Journal of Multivariate Analysis, Elsevier, vol. 196(C).
    6. 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.
    7. Amanda F. Mejia, 2022. "Discussion on “distributional independent component analysis for diverse neuroimaging modalities” by Ben Wu, Subhadip Pal, Jian Kang, and Ying Guo," Biometrics, The International Biometric Society, vol. 78(3), pages 1109-1112, September.
    8. Zhu, Xuwen & Melnykov, Volodymyr, 2018. "Manly transformation in finite mixture modeling," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 190-208.
    9. Lebret, Rémi & Iovleff, Serge & Langrognet, Florent & Biernacki, Christophe & Celeux, Gilles & Govaert, Gérard, 2015. "Rmixmod: The R Package of the Model-Based Unsupervised, Supervised, and Semi-Supervised Classification Mixmod Library," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 67(i06).
    10. 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.
    11. Fabian Dvorak, 2020. "stratEst: Strategy Estimation in R," TWI Research Paper Series 119, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
    12. repec:jss:jstsof:46:i06 is not listed on IDEAS
    13. Semhar Michael & Volodymyr Melnykov, 2016. "An effective strategy for initializing the EM algorithm in finite mixture models," 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. 10(4), pages 563-583, December.
    14. Hung Tong & Cristina Tortora, 2022. "Model-based clustering and outlier detection with missing data," 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 5-30, March.
    15. Xia Fan & Xiaowan Yang & Liming Chen, 2015. "Diversified resources and academic influence: patterns of university–industry collaboration in Chinese research-oriented universities," Scientometrics, Springer;Akadémiai Kiadó, vol. 104(2), pages 489-509, August.
    16. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "Erratum to: The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 327-355, July.
    17. Paolo Guarda & Abdelaziz Rouabah & John Theal, 2011. "An MVAR Framework to Capture Extreme Events in Macroprudential Stress Tests," BCL working papers 63, Central Bank of Luxembourg.
    18. 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).
    19. 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.
    20. Luca Scrucca & Adrian Raftery, 2015. "Improved initialisation of model-based clustering using Gaussian hierarchical partitions," 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 447-460, December.
    21. Nicosia, Aurélien & Duchesne, Thierry & Rivest, Louis-Paul & Fortin, Daniel, 2017. "A general hidden state random walk model for animal movement," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 76-95.

    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:56:y:2012:i:12:p:4122-4137. 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.