Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

Megane Boudineau, Herve Carfantan, Sebastien Bourguignon, Michael Bazot

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

Original languageEnglish (US)
Title of host publication2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016
PublisherIEEE Computer Society
Volume2016-August
ISBN (Electronic)9781467378024
DOIs
StatePublished - Aug 24 2016
Event19th IEEE Statistical Signal Processing Workshop, SSP 2016 - Palma de Mallorca, Spain
Duration: Jun 25 2016Jun 29 2016

Other

Other19th IEEE Statistical Signal Processing Workshop, SSP 2016
CountrySpain
CityPalma de Mallorca
Period6/25/166/29/16

Fingerprint

Bernoulli
Parameter estimation
Parameter Estimation
Sampling
Spectrum analysis
Markov processes
Sparse Approximation
Posterior Mean
Costs
Markov Chain Monte Carlo Algorithms
Gibbs Sampler
Approximation Problem
Gaussian Model
Hierarchical Model
Spectral Analysis
Sparsity
Linear Combination
Computational Cost
Model
Converge

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

Cite this

Boudineau, M., Carfantan, H., Bourguignon, S., & Bazot, M. (2016). Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models. In 2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016 (Vol. 2016-August). [7551706] IEEE Computer Society. https://doi.org/10.1109/SSP.2016.7551706

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models. / Boudineau, Megane; Carfantan, Herve; Bourguignon, Sebastien; Bazot, Michael.

2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016. Vol. 2016-August IEEE Computer Society, 2016. 7551706.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Boudineau, M, Carfantan, H, Bourguignon, S & Bazot, M 2016, Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models. in 2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016. vol. 2016-August, 7551706, IEEE Computer Society, 19th IEEE Statistical Signal Processing Workshop, SSP 2016, Palma de Mallorca, Spain, 6/25/16. https://doi.org/10.1109/SSP.2016.7551706
Boudineau M, Carfantan H, Bourguignon S, Bazot M. Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models. In 2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016. Vol. 2016-August. IEEE Computer Society. 2016. 7551706 https://doi.org/10.1109/SSP.2016.7551706
Boudineau, Megane ; Carfantan, Herve ; Bourguignon, Sebastien ; Bazot, Michael. / Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models. 2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016. Vol. 2016-August IEEE Computer Society, 2016.
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