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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