Direct density-derivative estimation
- Authors
- Sasaki, Hiroaki; Noh, Yung-Kyun; Niu, Gang; Sugiyama, Masashi
- Issue Date
- Jun-2016
- Publisher
- MIT PRESS
- Citation
- NEURAL COMPUTATION, v.28, no.6, pp.1101 - 1140
- Indexed
- SCIE
SCOPUS
- Journal Title
- NEURAL COMPUTATION
- Volume
- 28
- Number
- 6
- Start Page
- 1101
- End Page
- 1140
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/154408
- DOI
- 10.1162/NECO_a_00835
- ISSN
- 0899-7667
- 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.
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