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ISSN
0899-7667
E-ISSN
1530-888X
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2.21

Neural Computation

June 2016, Vol. 28, No. 6, Pages 1101-1140
(doi: 10.1162/NECO_a_00835)
© 2016 Massachusetts Institute of Technology
Direct Density Derivative Estimation
Article PDF (1.12 MB)
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.