<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Institute of Computer Science Pozna´n University of Technology, Piotrowo 2, 60-965 Poznan, Poland

Institute of Computer Science and Electronics University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland

University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland

International Journal of Applied Mathematics and Computer Science

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...

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

Published Online: Dec 31, 2013

Page range: 869 - 885

DOI: https://doi.org/10.2478/amcs-2013-0065

This content is open access.