Nonparametric e-Mixture Estimation.
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 [Formula: see text]- and [Formula: see text]-mixtures. The [Formula: see text]-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 [Formula: see text]-mixture is rarely used because of its difficulty of estimation, particularly for nonparametric models. The [Formula: see text]-mixture, however, is a well-tempered 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 [Formula: see text]-mixture 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.
Graduate School of Advanced Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan ken.takano@toki.waseda.jp.
Ken
K
Takano
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan hinohide@cs.tsukuba.ac.jp.
Hideitsu
H
Hino
National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568, Japan s.akaho@aist.go.jp.
Shotaro
S
Akaho
Graduate School of Advanced Science and Engineering, Waseda University, Shinjuku, Tokyo 169-8555, Japan noboru.murata@eb.waseda.ac.jp.
Noboru
N
Murata