Asymptotic Properties of Recursive Maximum Likelihood Estimation in Non-Linear State-Space Models

Aug 01, 2018

Vladislav Z. B. Tadic, Arnaud Doucet

Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Poyiadjis, Doucet and Singh, Biometrika 2018], a recursive maximum likelihood algorithm based on a particle approximation to the optimal filter derivative has been proposed and studied through numerical simulations. Here, this algorithm and its asymptotic behavior are analyzed theoretically. We show that the algorithm accurately estimates maxima to the underlying (average) log-likelihood when the number of particles is sufficiently large. We also derive (relatively) tight bounds on the estimation error. The obtained results hold under (relatively) mild conditions and cover several classes of non-linear state-space models met in practice.
Aug 01, 2018

Vladislav Z. B. Tadic, Arnaud Doucet

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* Proceedings of the 31st International Conference on Machine Learning, JMLR W&CP 32 (2) 2014

* 9 pages, 4 figures

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Efficient Bayesian Inference for Generalized Bradley-Terry Models

Nov 08, 2010

Francois Caron, Arnaud Doucet

Nov 08, 2010

Francois Caron, Arnaud Doucet

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The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and Lojasiewicz inequality), tight bounds on the asymptotic bias of the iterates generated by such an algorithm are derived. The obtained results hold under mild conditions and cover a broad class of high-dimensional nonlinear algorithms. Using these results, the asymptotic properties of the policy-gradient (reinforcement) learning and adaptive population Monte Carlo sampling are studied. Relying on the same results, the asymptotic behavior of the recursive maximum split-likelihood estimation in hidden Markov models is analyzed, too.

* arXiv admin note: text overlap with arXiv:0907.1020

* arXiv admin note: text overlap with arXiv:0907.1020

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On the Impact of the Activation Function on Deep Neural Networks Training

Feb 19, 2019

Soufiane Hayou, Arnaud Doucet, Judith Rousseau

Feb 19, 2019

Soufiane Hayou, Arnaud Doucet, Judith Rousseau

* 35 pages

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On the Selection of Initialization and Activation Function for Deep Neural Networks

Oct 07, 2018

Soufiane Hayou, Arnaud Doucet, Judith Rousseau

Oct 07, 2018

Soufiane Hayou, Arnaud Doucet, Judith Rousseau

* 8 pages, 15 figures

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On Markov chain Monte Carlo methods for tall data

May 11, 2015

Rémi Bardenet, Arnaud Doucet, Chris Holmes

May 11, 2015

Rémi Bardenet, Arnaud Doucet, Chris Holmes

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Sparsity-Promoting Bayesian Dynamic Linear Models

Mar 01, 2012

François Caron, Luke Bornn, Arnaud Doucet

Mar 01, 2012

François Caron, Luke Bornn, Arnaud Doucet

* N° RR-7895 (2012)

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Hamiltonian Variational Auto-Encoder

May 29, 2018

Anthony L. Caterini, Arnaud Doucet, Dino Sejdinovic

May 29, 2018

Anthony L. Caterini, Arnaud Doucet, Dino Sejdinovic

* Submitted to NIPS 2018

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* submitted to NIPS 2015

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Reversible Jump MCMC Simulated Annealing for Neural Networks

Jan 16, 2013

Christophe Andrieu, Nando de Freitas, Arnaud Doucet

Jan 16, 2013

Christophe Andrieu, Nando de Freitas, Arnaud Doucet

* Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)

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Toward Practical N2 Monte Carlo: the Marginal Particle Filter

Jul 04, 2012

Mike Klaas, Nando de Freitas, Arnaud Doucet

Jul 04, 2012

Mike Klaas, Nando de Freitas, Arnaud Doucet

* Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005)

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Bayesian nonparametric image segmentation using a generalized Swendsen-Wang algorithm

Feb 09, 2016

Richard Yi Da Xu, Francois Caron, Arnaud Doucet

Feb 09, 2016

Richard Yi Da Xu, Francois Caron, Arnaud Doucet

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Unbiased Smoothing using Particle Independent Metropolis-Hastings

Feb 05, 2019

Lawrence Middleton, George Deligiannidis, Arnaud Doucet, Pierre E. Jacob

Feb 05, 2019

Lawrence Middleton, George Deligiannidis, Arnaud Doucet, Pierre E. Jacob

* 13 pages

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Asynchronous Anytime Sequential Monte Carlo

Jul 10, 2014

Brooks Paige, Frank Wood, Arnaud Doucet, Yee Whye Teh

Jul 10, 2014

Brooks Paige, Frank Wood, Arnaud Doucet, Yee Whye Teh

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Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks

Jan 16, 2013

Arnaud Doucet, Nando de Freitas, Kevin Murphy, Stuart Russell

Jan 16, 2013

Arnaud Doucet, Nando de Freitas, Kevin Murphy, Stuart Russell

* Appears in Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence (UAI2000)

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New inference strategies for solving Markov Decision Processes using reversible jump MCMC

May 09, 2012

Matthias Hoffman, Hendrik Kueck, Nando de Freitas, Arnaud Doucet

May 09, 2012

Matthias Hoffman, Hendrik Kueck, Nando de Freitas, Arnaud Doucet

* Appears in Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI2009)

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Scalable Metropolis-Hastings for Exact Bayesian Inference with Large Datasets

Jan 30, 2019

Robert Cornish, Paul Vanetti, Alexandre Bouchard-Côté, George Deligiannidis, Arnaud Doucet

Jan 30, 2019

Robert Cornish, Paul Vanetti, Alexandre Bouchard-Côté, George Deligiannidis, Arnaud Doucet

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