
Statistics Papers
Document Type
Technical Report
Date of this Version
2010
Publication Source
Journal of Computational and Graphical Studies
Volume
19
Issue
1
Start Page
205
Last Page
220
DOI
10.1198/jcgs.2010.09046
Abstract
The computational complexity of evaluating the kernel density estimate (or its derivatives) at m evaluation points given n sample points scales quadratically as O(nm)—making it prohibitively expensive for large datasets. While approximate methods like binning could speed up the computation, they lack a precise control over the accuracy of the approximation. There is no straightforward way of choosing the binning parameters a priori in order to achieve a desired approximation error. We propose a novel computationally efficient ε-exact approximation algorithm for the univariate Gaussian kernel-based density derivative estimation that reduces the computational complexity from O(nm) to linear O(n+m). The user can specify a desired accuracy ε. The algorithm guarantees that the actual error between the approximation and the original kernel estimate will always be less than ε. We also apply our proposed fast algorithm to speed up automatic bandwidth selection procedures. We compare our method to the best available binning methods in terms of the speed and the accuracy. Our experimental results show that the proposed method is almost twice as fast as the best binning methods and is around five orders of magnitude more accurate. The software for the proposed method is available online.
Copyright/Permission Statement
This is an Accepted Manuscript of an article published by Taylor & Francis in the Journal of Computational and Graphical Studies in 2010, available online: http://dx.doi.org/10.1198/jcgs.2010.09046
Keywords
bandwidth estimation, binning, fast Fourier transform, kernel density derivative estimation, kernel density estimation
Recommended Citation
Raykar, V. C., Duraiswami, R., & Zhao, L. H. (2010). Fast Computation of Kernel Estimators. Journal of Computational and Graphical Studies, 19 (1), 205-220. http://dx.doi.org/10.1198/jcgs.2010.09046
Included in
Applied Mathematics Commons, Business Commons, Mathematics Commons, Statistics and Probability Commons
Date Posted: 25 October 2018
This document has been peer reviewed.