### Abstract

In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty term in the cost function of the estimation problem through the use of an appropriate prior distribution, we show how the EM algorithm can be used to efficiently solve the corresponding optimization problem. To this end, we rely on variance-mean Gaussian mixtures (VMGM) to describe the prior distribution, while we incorporate many nice features of these mixtures to our estimation problem. The corresponding MAP estimation problem is completely expressed in terms of the EM algorithm, which allows for handling nonlinearities and hidden variables that cannot be easily handled with traditional methods. For comparison purposes, we also develop a Coordinate Descent algorithm for the ℓ_{q}-norm penalized problem and present the performance results via simulations.

Original language | English (US) |
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Title of host publication | 2015 IEEE International Workshop on Machine Learning for Signal Processing - Proceedings of MLSP 2015 |

Editors | Deniz Erdogmus, Serdar Kozat, Jan Larsen, Murat Akcakaya |

Publisher | IEEE Computer Society |

ISBN (Electronic) | 9781467374545 |

DOIs | |

State | Published - Nov 10 2015 |

Event | 25th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2015 - Boston, United States Duration: Sep 17 2015 → Sep 20 2015 |

### Publication series

Name | IEEE International Workshop on Machine Learning for Signal Processing, MLSP |
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Volume | 2015-November |

ISSN (Print) | 2161-0363 |

ISSN (Electronic) | 2161-0371 |

### Conference

Conference | 25th IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2015 |
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Country | United States |

City | Boston |

Period | 9/17/15 → 9/20/15 |

### Keywords

- Convergence
- Maximum likelihood estimation
- Optimization
- Parameter estimation
- Probability density function
- Signal processing algorithms

### ASJC Scopus subject areas

- Human-Computer Interaction
- Signal Processing

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## Cite this

_{q}-norm regularized sparse parameter estimation using the em algorithm. In D. Erdogmus, S. Kozat, J. Larsen, & M. Akcakaya (Eds.),

*2015 IEEE International Workshop on Machine Learning for Signal Processing - Proceedings of MLSP 2015*[7324321] (IEEE International Workshop on Machine Learning for Signal Processing, MLSP; Vol. 2015-November). IEEE Computer Society. https://doi.org/10.1109/MLSP.2015.7324321