IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i8p2375-2387.html
   My bibliography  Save this article

Variational Bayes approach for model aggregation in unsupervised classification with Markovian dependency

Author

Listed:
  • Volant, Stevenn
  • Martin Magniette, Marie-Laure
  • Robin, Stéphane

Abstract

A binary unsupervised classification problem where each observation is associated with an unobserved label that needs to be retrieved is considered. More precisely, it is assumed that there are two groups of observation: normal and abnormal. The ‘normal’ observations are coming from a known distribution whereas the distribution of the ‘abnormal’ observations is unknown. Several models have been developed to fit this unknown distribution. An alternative based on a mixture of Gaussian distributions is proposed. The inference is performed within a variational Bayesian framework and the aim is to infer the posterior probability of belonging to the class of interest. To this end, it makes little sense to estimate the number of mixture components since each mixture model provides more or less relevant information to the posterior probability estimation. By computing a weighted average (named aggregated estimator) over the model collection, Bayesian Model Averaging (BMA) is one way of combining models in order to account for information provided by each model. An aim is then the estimation of the weights and the posterior probability for a specific model. Optimal approximations of these quantities from the variational theory are derived; other approximations of the weights are also proposed. It is assumed that the data are dependent (Markovian dependency) and hence a Hidden Markov Model is considered. A simulation study is carried out to evaluate the accuracy of the estimates in terms of classification performance. An illustration on both epidemiologic and genetic datasets is presented.

Suggested Citation

  • Volant, Stevenn & Martin Magniette, Marie-Laure & Robin, Stéphane, 2012. "Variational Bayes approach for model aggregation in unsupervised classification with Markovian dependency," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2375-2387.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2375-2387
    DOI: 10.1016/j.csda.2012.01.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000710
    Download Restriction: Full text for ScienceDirect subscribers only.

    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. Ren, Qian & Banerjee, Sudipto & Finley, Andrew O. & Hodges, James S., 2011. "Variational Bayesian methods for spatial data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3197-3217, December.
    2. Bérard Caroline & Martin-Magniette Marie-Laure & Brunaud Véronique & Aubourg Sébastien & Robin Stéphane, 2011. "Unsupervised Classification for Tiling Arrays: ChIP-chip and Transcriptome," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 10(1), pages 1-22, November.
    3. Robin, Stephane & Bar-Hen, Avner & Daudin, Jean-Jacques & Pierre, Laurent, 2007. "A semi-parametric approach for mixture models: Application to local false discovery rate estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5483-5493, August.
    4. Wenguang Sun & T. Tony Cai, 2009. "Large-scale multiple testing under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 393-424.
    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. Liu, Shen & Maharaj, Elizabeth Ann & Inder, Brett, 2014. "Polarization of forecast densities: A new approach to time series classification," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 345-361.

    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:8:p:2375-2387. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/csda .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.