### 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 language | English (US) |
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Title of host publication | 2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016 |

Publisher | IEEE Computer Society |

Volume | 2016-August |

ISBN (Electronic) | 9781467378024 |

DOIs | |

State | Published - Aug 24 2016 |

Event | 19th IEEE Statistical Signal Processing Workshop, SSP 2016 - Palma de Mallorca, Spain Duration: Jun 25 2016 → Jun 29 2016 |

### Other

Other | 19th IEEE Statistical Signal Processing Workshop, SSP 2016 |
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Country | Spain |

City | Palma de Mallorca |

Period | 6/25/16 → 6/29/16 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

AU - Boudineau, Megane

AU - Carfantan, Herve

AU - Bourguignon, Sebastien

AU - Bazot, Michael

PY - 2016/8/24

Y1 - 2016/8/24

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84987864228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987864228&partnerID=8YFLogxK

U2 - 10.1109/SSP.2016.7551706

DO - 10.1109/SSP.2016.7551706

M3 - Conference contribution

VL - 2016-August

BT - 2016 19th IEEE Statistical Signal Processing Workshop, SSP 2016

PB - IEEE Computer Society

ER -