title: Direct Density Derivative Estimation.
abstract: Estimating the derivatives of probability density functions is an essential step in statistical data analysis. A naive approach to estimate the derivatives is to first perform density estimation and then compute its derivatives. However, this approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator. To cope with this problem, in this letter, we propose a novel method that directly estimates density derivatives without going through density estimation. The proposed method provides computationally efficient estimation for the derivatives of any order on multidimensional data with a hyperparameter tuning method and achieves the optimal parametric convergence rate. We further discuss an extension of the proposed method by applying regularized multitask learning and a general framework for density derivative estimation based on Bregman divergences. Applications of the proposed method to nonparametric Kullback-Leibler divergence approximation and bandwidth matrix selection in kernel density estimation are also explored.
authors.affiliation: Graduate School of Information Science, Nara Institute of Science and Technology, Nara 630-0192, Japan hsasaki@is.naist.jp.
authors.forename: Hiroaki
authors.initials: H
authors.lastname: Sasaki
authors.affiliation: Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea nohyung@snu.ac.kr.
authors.forename: Yung-Kyun
authors.initials: YK
authors.lastname: Noh
authors.affiliation: Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan gang@ms.k.u-tokyo.ac.jp.
authors.forename: Gang
authors.initials: G
authors.lastname: Niu
authors.affiliation: Graduate School of Frontier Sciences, University of Tokyo, Tokyo 113-0033, Japan sugi@k.u-tokyo.ac.jp.
authors.forename: Masashi
authors.initials: M
authors.lastname: Sugiyama