Team : mistis
Section: Scientific Foundations
Keywords : missing data, mixture of distributions, EM algorithm, stochastic algorithms, selection and combination of models, statistical pattern recognition, image analysis, hidden Markov field, Bayesian inference.
Hidden Markov chains or hidden Markov fields correspond to cases where the zi's are distributed according to a Markov chain or a Markov field. These models are widely used in signal processing (speech recognition, genome sequence analysis) and in image processing (remote sensing, MRI, etc.). Markovian models are part of graphical models. In these models, the variable organization can be represented by a graph where the nodes represent the variables and the edges the statistical dependencies between the variables. The graphs can be either directed, e.g. Bayesian Networks, or undirected, e.g. Markov Random Fields. The specificity of Markovian models is that the dependencies between the nodes are limited to the nearest neighbor nodes. The neighborhood definition can vary and be adapted to the problem of interest. When parts of the variables (nodes) are not observed, we refer to these models as Hidden Markov Models (HMM). Such models are very flexible in practice and can naturally account for the phenomena to be studied. They are very useful in modelling spatial dependencies but these dependencies and the possible existence of hidden variables are also responsible for a typically large amount of computation. It follows that the statistical analysis may not be straightforward but we propose to use variational approximations for estimation and model selection when exact calculations are intractable. Many experiments have to be carried out to assess the approximations quality and the associated estimation methods performance before addressing theoretical properties such as convergence and speed results.