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


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


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

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    References listed on IDEAS

    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.
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    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.


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