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We consider a binary unsupervised classification problem where eachobservation is associated with an unobserved label that we want to retrieve.More precisely, we assume that there are two groups of observation: normal andabnormal. The `normal' observations are coming from a known distributionwhereas the distribution of the `abnormal' observations is unknown. Severalmodels have been developed to fit this unknown distribution. In this paper, wepropose an alternative based on a mixture of Gaussian distributions. Theinference is done within a variational Bayesian framework and our aim is toinfer the posterior probability of belonging to the class of interest. To thisend, it makes no sense to estimate the mixture component number since eachmixture model provides more or less relevant information to the posteriorprobability estimation. By computing a weighted average (named aggregatedestimator) over the model collection, Bayesian Model Averaging (BMA) is one wayof combining models in order to account for information provided by each model.The aim is then the estimation of the weights and the posterior probability forone specific model. In this work, we derive optimal approximations of thesequantities from the variational theory and propose other approximations of theweights. To perform our method, we consider that the data are dependent(Markovian dependency) and hence we consider a Hidden Markov Model. Asimulation study is carried out to evaluate the accuracy of the estimates interms of classification. We also present an application to the analysis ofpublic health surveillance systems.

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