### Abstract

Modal linear regression (MLR) is a standard method for modeling the conditional mode of a response variable using a linear combination of explanatory variables. It is effective when dealing with response variables with an asymmetric, multi-modal distribution. Because of the nonparametric nature of MLR, it is difficult to construct a statistical model manifold in the sense of information geometry. In this work, a model manifold is constructed using observations instead of explicit parametric models. We also propose a method for constructing a data manifold based on an empirical distribution. The em algorithm, which is a geometric formulation of the EM algorithm, of MLR is shown to be equivalent to the conventional EM algorithm of MLR.

Original language | English |
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Title of host publication | Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings |

Editors | Long Cheng, Seiichi Ozawa, Andrew Chi Sing Leung |

Publisher | Springer-Verlag |

Pages | 535-545 |

Number of pages | 11 |

ISBN (Print) | 9783030041816 |

DOIs | |

Publication status | Published - 2018 Jan 1 |

Event | 25th International Conference on Neural Information Processing, ICONIP 2018 - Siem Reap, Cambodia Duration: 2018 Dec 13 → 2018 Dec 16 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11303 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 25th International Conference on Neural Information Processing, ICONIP 2018 |
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Country | Cambodia |

City | Siem Reap |

Period | 18/12/13 → 18/12/16 |

### Fingerprint

### Keywords

- EM algorithm
- Information geometry
- Modal linear regression

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings*(pp. 535-545). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11303 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-030-04182-3_47

**Information geometric perspective of modal linear regression.** / Sando, Keishi; Akaho, Shotaro; Murata, Noboru; Hino, Hideitsu.

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

*Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11303 LNCS, Springer-Verlag, pp. 535-545, 25th International Conference on Neural Information Processing, ICONIP 2018, Siem Reap, Cambodia, 18/12/13. https://doi.org/10.1007/978-3-030-04182-3_47

}

TY - GEN

T1 - Information geometric perspective of modal linear regression

AU - Sando, Keishi

AU - Akaho, Shotaro

AU - Murata, Noboru

AU - Hino, Hideitsu

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Modal linear regression (MLR) is a standard method for modeling the conditional mode of a response variable using a linear combination of explanatory variables. It is effective when dealing with response variables with an asymmetric, multi-modal distribution. Because of the nonparametric nature of MLR, it is difficult to construct a statistical model manifold in the sense of information geometry. In this work, a model manifold is constructed using observations instead of explicit parametric models. We also propose a method for constructing a data manifold based on an empirical distribution. The em algorithm, which is a geometric formulation of the EM algorithm, of MLR is shown to be equivalent to the conventional EM algorithm of MLR.

AB - Modal linear regression (MLR) is a standard method for modeling the conditional mode of a response variable using a linear combination of explanatory variables. It is effective when dealing with response variables with an asymmetric, multi-modal distribution. Because of the nonparametric nature of MLR, it is difficult to construct a statistical model manifold in the sense of information geometry. In this work, a model manifold is constructed using observations instead of explicit parametric models. We also propose a method for constructing a data manifold based on an empirical distribution. The em algorithm, which is a geometric formulation of the EM algorithm, of MLR is shown to be equivalent to the conventional EM algorithm of MLR.

KW - EM algorithm

KW - Information geometry

KW - Modal linear regression

UR - http://www.scopus.com/inward/record.url?scp=85059008645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059008645&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-04182-3_47

DO - 10.1007/978-3-030-04182-3_47

M3 - Conference contribution

AN - SCOPUS:85059008645

SN - 9783030041816

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 535

EP - 545

BT - Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings

A2 - Cheng, Long

A2 - Ozawa, Seiichi

A2 - Leung, Andrew Chi Sing

PB - Springer-Verlag

ER -