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Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures

François Caron 1 Manuel Davy 1, 2 Arnaud Doucet 3 Emmanuel Duflos 1, 2 Philippe Vanheeghe 1, 2
1 SEQUEL - Sequential Learning
LIFL - Laboratoire d'Informatique Fondamentale de Lille, LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal, Inria Lille - Nord Europe
2 LAGIS-SI
LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
Abstract : Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced. Efficient Markov chain Monte Carlo and Sequential Monte Carlo methods are then developed to perform optimal batch and sequential estimation in such contexts. The algorithms are applied to blind deconvolution and change point detection. Experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts.
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Submitted on : Thursday, February 8, 2007 - 5:16:51 PM
Last modification on : Thursday, January 20, 2022 - 4:12:36 PM
Long-term archiving on: : Tuesday, April 6, 2010 - 11:40:19 PM

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François Caron, Manuel Davy, Arnaud Doucet, Emmanuel Duflos, Philippe Vanheeghe. Bayesian Inference for Linear Dynamic Models with Dirichlet Process Mixtures. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2008, 56 (1), pp.71-84. ⟨10.1109/TSP.2007.900167⟩. ⟨inria-00129646⟩

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