### 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 |

### Keywords

- EM algorithm
- Information geometry
- Modal linear regression

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## 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