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
2 LAGIS-SI
3 UBC Statistics - Department of Statistics [Vancouver]

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.

Mots clés: Bayesian nonparametrics; Dirichlet process mixture (DPM); Markov chain Monte Carlo (MCMC); particle filter; Rao-Blackwellization

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

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, 2008, 56 (1), pp.71-84. ⟨10.1109/TSP.2007.900167⟩. ⟨inria-00129646⟩