# Graphics processing units in acceleration of bandwidth selection for kernel density estimation

• Volume: 23, Issue: 4, page 869-885
• ISSN: 1641-876X

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## Abstract

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The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.

## How to cite

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Witold Andrzejewski, Artur Gramacki, and Jarosław Gramacki. "Graphics processing units in acceleration of bandwidth selection for kernel density estimation." International Journal of Applied Mathematics and Computer Science 23.4 (2013): 869-885. <http://eudml.org/doc/262420>.

@article{WitoldAndrzejewski2013,
abstract = {The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.},
author = {Witold Andrzejewski, Artur Gramacki, Jarosław Gramacki},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {bandwidth selection; graphics processing unit; probability density function; nonparametric estimation; kernel estimation},
language = {eng},
number = {4},
pages = {869-885},
title = {Graphics processing units in acceleration of bandwidth selection for kernel density estimation},
url = {http://eudml.org/doc/262420},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Witold Andrzejewski
AU - Artur Gramacki
AU - Jarosław Gramacki
TI - Graphics processing units in acceleration of bandwidth selection for kernel density estimation
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 4
SP - 869
EP - 885
AB - The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.
LA - eng
KW - bandwidth selection; graphics processing unit; probability density function; nonparametric estimation; kernel estimation
UR - http://eudml.org/doc/262420
ER -

## References

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