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Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach

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Chiappa,  S
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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MPIK-TR-161.pdf
(Publisher version), 532KB

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Citation

Chiappa, S., & Barber, D.(2007). Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach (161). Tübingen, Germany: Max Planck Institute for Biological Cybernetics.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CE85-7
Abstract
We describe two related models to cluster multidimensional time-series under the assumption of an underlying linear Gaussian dynamical process. In the first model, times-series are assigned to the same cluster when they show global similarity in their dynamics, while in the second model times-series are assigned to the same cluster when they show simultaneous similarity. Both models are based on Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models in order to (semi) automatically determine an appropriate number of components in the mixture, and to additionally bias the components to a parsimonious parameterization. The resulting models are formally intractable and to deal with this we describe a deterministic approximation based on a novel implementation of Variational Bayes.