### Abstract

The hierarchical mixture of experts (HME) is a tree-structured probabilistic model for regression and classification. The HME has a considerable expression capability, however, the estimation of the parameters tends to overfit due to the complexity of the model. To avoid this problem, regularization techniques are widely used. In particular, it is known that a sparse solution can be obtained by L1 regularization. From a Bayesian point of view, regularization techniques are equivalent to assume that the parameters follow prior distributions and find the maximum a posteriori probability estimator. It is known that L1 regularization is equivalent to assuming Laplace distributions as prior distributions. However, it is difficult to compute the posterior distribution if Laplace distributions are assumed. In this paper, we assume that the parameters of the HME follow hierarchical prior distributions which are equivalent to Laplace distribution to promote sparse solutions. We propose a Bayesian estimation algorithm based on the variational method. Finally, the proposed algorithm is evaluated by computer simulations.

Original language | English |
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Title of host publication | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 60-64 |

Number of pages | 5 |

ISBN (Electronic) | 9784885523182 |

DOIs | |

Publication status | Published - 2019 Mar 8 |

Event | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 - Singapore, Singapore Duration: 2018 Oct 28 → 2018 Oct 31 |

### Publication series

Name | Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018 |
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### Conference

Conference | 15th International Symposium on Information Theory and Its Applications, ISITA 2018 |
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Country | Singapore |

City | Singapore |

Period | 18/10/28 → 18/10/31 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science Applications
- Information Systems

### Cite this

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018*(pp. 60-64). [8664333] (Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ISITA.2018.8664333

**Sparse Bayesian Hierarchical Mixture of Experts and Variational Inference.** / Iikubo, Yuji; Horii, Shunsuke; Matsushima, Toshiyasu.

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

*Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018.*, 8664333, Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018, Institute of Electrical and Electronics Engineers Inc., pp. 60-64, 15th International Symposium on Information Theory and Its Applications, ISITA 2018, Singapore, Singapore, 18/10/28. https://doi.org/10.23919/ISITA.2018.8664333

}

TY - GEN

T1 - Sparse Bayesian Hierarchical Mixture of Experts and Variational Inference

AU - Iikubo, Yuji

AU - Horii, Shunsuke

AU - Matsushima, Toshiyasu

PY - 2019/3/8

Y1 - 2019/3/8

N2 - The hierarchical mixture of experts (HME) is a tree-structured probabilistic model for regression and classification. The HME has a considerable expression capability, however, the estimation of the parameters tends to overfit due to the complexity of the model. To avoid this problem, regularization techniques are widely used. In particular, it is known that a sparse solution can be obtained by L1 regularization. From a Bayesian point of view, regularization techniques are equivalent to assume that the parameters follow prior distributions and find the maximum a posteriori probability estimator. It is known that L1 regularization is equivalent to assuming Laplace distributions as prior distributions. However, it is difficult to compute the posterior distribution if Laplace distributions are assumed. In this paper, we assume that the parameters of the HME follow hierarchical prior distributions which are equivalent to Laplace distribution to promote sparse solutions. We propose a Bayesian estimation algorithm based on the variational method. Finally, the proposed algorithm is evaluated by computer simulations.

AB - The hierarchical mixture of experts (HME) is a tree-structured probabilistic model for regression and classification. The HME has a considerable expression capability, however, the estimation of the parameters tends to overfit due to the complexity of the model. To avoid this problem, regularization techniques are widely used. In particular, it is known that a sparse solution can be obtained by L1 regularization. From a Bayesian point of view, regularization techniques are equivalent to assume that the parameters follow prior distributions and find the maximum a posteriori probability estimator. It is known that L1 regularization is equivalent to assuming Laplace distributions as prior distributions. However, it is difficult to compute the posterior distribution if Laplace distributions are assumed. In this paper, we assume that the parameters of the HME follow hierarchical prior distributions which are equivalent to Laplace distribution to promote sparse solutions. We propose a Bayesian estimation algorithm based on the variational method. Finally, the proposed algorithm is evaluated by computer simulations.

UR - http://www.scopus.com/inward/record.url?scp=85063870175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063870175&partnerID=8YFLogxK

U2 - 10.23919/ISITA.2018.8664333

DO - 10.23919/ISITA.2018.8664333

M3 - Conference contribution

AN - SCOPUS:85063870175

T3 - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

SP - 60

EP - 64

BT - Proceedings of 2018 International Symposium on Information Theory and Its Applications, ISITA 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -