### Abstract

This study considers the common situation in data analysis when there are few observations of the distribution of interest or the target distribution, while abundant observations are available from auxiliary distributions. In this situation, it is natural to compensate for the lack of data from the target distribution by using data sets from these auxiliary distributions-in other words, approximating the target distribution in a subspace spanned by a set of auxiliary distributions. Mixture modeling is one of the simplest ways to integrate information from the target and auxiliary distributions in order to express the target distribution as accurately as possible. There are two typical mixtures in the context of information geometry: the m- and e-mixtures. The m-mixture is applied in a variety of research fields because of the presence of the well-known expectation-maximazation algorithm for parameter estimation, whereas the e-mixture is rarely used because of its difficulty of estimation, particularly for nonparametric models. The e-mixture, however, is a welltempered distribution that satisfies the principle of maximum entropy. To model a target distribution with scarce observations accurately, this letter proposes a novel framework for a nonparametric modeling of the emixture and a geometrically inspired estimation algorithm. As numerical examples of the proposed framework, a transfer learning setup is considered. The experimental results show that this framework works well for three types of synthetic data sets, as well as an EEG real-world data set.

Original language | English |
---|---|

Pages (from-to) | 2687-2725 |

Number of pages | 39 |

Journal | Neural Computation |

Volume | 28 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2016 Dec 1 |

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### ASJC Scopus subject areas

- Arts and Humanities (miscellaneous)
- Cognitive Neuroscience

### Cite this

*Neural Computation*,

*28*(12), 2687-2725. https://doi.org/10.1162/NECO_a_00888

**Nonparametric e-mixture estimation.** / Takano, Ken; Hino, Hideitsu; Akaho, Shotaro; Murata, Noboru.

Research output: Contribution to journal › Letter

*Neural Computation*, vol. 28, no. 12, pp. 2687-2725. https://doi.org/10.1162/NECO_a_00888

}

TY - JOUR

T1 - Nonparametric e-mixture estimation

AU - Takano, Ken

AU - Hino, Hideitsu

AU - Akaho, Shotaro

AU - Murata, Noboru

PY - 2016/12/1

Y1 - 2016/12/1

N2 - This study considers the common situation in data analysis when there are few observations of the distribution of interest or the target distribution, while abundant observations are available from auxiliary distributions. In this situation, it is natural to compensate for the lack of data from the target distribution by using data sets from these auxiliary distributions-in other words, approximating the target distribution in a subspace spanned by a set of auxiliary distributions. Mixture modeling is one of the simplest ways to integrate information from the target and auxiliary distributions in order to express the target distribution as accurately as possible. There are two typical mixtures in the context of information geometry: the m- and e-mixtures. The m-mixture is applied in a variety of research fields because of the presence of the well-known expectation-maximazation algorithm for parameter estimation, whereas the e-mixture is rarely used because of its difficulty of estimation, particularly for nonparametric models. The e-mixture, however, is a welltempered distribution that satisfies the principle of maximum entropy. To model a target distribution with scarce observations accurately, this letter proposes a novel framework for a nonparametric modeling of the emixture and a geometrically inspired estimation algorithm. As numerical examples of the proposed framework, a transfer learning setup is considered. The experimental results show that this framework works well for three types of synthetic data sets, as well as an EEG real-world data set.

AB - This study considers the common situation in data analysis when there are few observations of the distribution of interest or the target distribution, while abundant observations are available from auxiliary distributions. In this situation, it is natural to compensate for the lack of data from the target distribution by using data sets from these auxiliary distributions-in other words, approximating the target distribution in a subspace spanned by a set of auxiliary distributions. Mixture modeling is one of the simplest ways to integrate information from the target and auxiliary distributions in order to express the target distribution as accurately as possible. There are two typical mixtures in the context of information geometry: the m- and e-mixtures. The m-mixture is applied in a variety of research fields because of the presence of the well-known expectation-maximazation algorithm for parameter estimation, whereas the e-mixture is rarely used because of its difficulty of estimation, particularly for nonparametric models. The e-mixture, however, is a welltempered distribution that satisfies the principle of maximum entropy. To model a target distribution with scarce observations accurately, this letter proposes a novel framework for a nonparametric modeling of the emixture and a geometrically inspired estimation algorithm. As numerical examples of the proposed framework, a transfer learning setup is considered. The experimental results show that this framework works well for three types of synthetic data sets, as well as an EEG real-world data set.

UR - http://www.scopus.com/inward/record.url?scp=84997769361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84997769361&partnerID=8YFLogxK

U2 - 10.1162/NECO_a_00888

DO - 10.1162/NECO_a_00888

M3 - Letter

VL - 28

SP - 2687

EP - 2725

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 12

ER -