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Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach
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.
@techreport{4917, title = {Dirichlet Mixtures of Bayesian Linear Gaussian State-Space Models: a Variational Approach}, 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.}, number = {161}, organization = {Max-Planck-Gesellschaft}, institution = {Max Planck Institute for Biological Cybernetics, Tübingen, Germany}, school = {Biologische Kybernetik}, month = mar, year = {2007}, slug = {4917}, author = {Chiappa, S. and Barber, D.}, month_numeric = {3} }