[1B3-GS-2] Machine learning

[1B3-GS-2-05] Fully Data-driven Normalized and Exponentiated Kernel Density Estimator with Hyvärinen Score

〇Shouto Yonekura¹, Shunsuke Imai², Yoshihiko Nishiyama², Shonosuke Sugasawa³, Takuya Koriyama⁴ (1. Kodansha Ltd., 2. Univ. of Kyoto, 3. Univ. of Tokyo, 4. Rutgers University)

Keywords: Density estimation, Fisher divergence, Hyvärinen Score

We introduce a new deal of kernel density estimation using an exponentiated
form of kernel density estimators. The density estimator has two hyperparameters
flexibly controlling the smoothness of the resulting density. We tune them in a datadriven manner by minimizing an objective function based on the Hyvärinen score
to avoid the optimization involving the intractable normalizing constant due to the
exponentiation. We show the asymptotic properties of the proposed estimator and
emphasize the importance of including the two hyperparameters for flexible density
estimation. Our simulation studies and application to income data show that the
proposed density estimator is appealing when the underlying density is multi-modal
or observations contain outliers.