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

2013 ◽  
Vol 23 (4) ◽  
pp. 869-885 ◽  
Author(s):  
Witold Andrzejewski ◽  
Artur Gramacki ◽  
Jarosław Gramacki
Keyword(s):  
Graphics Processing Units ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Data Driven ◽  
Density Estimator ◽  
Algorithmic Optimization ◽  
Bandwidth Parameter ◽  
Selection For ◽  
Graphics Processing ◽  
Probability Density Function Pdf

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.

scholarly journals Optimal bandwidth selection for recursive Gumbel kernel density estimators

2019 ◽  
Vol 7 (1) ◽  
pp. 375-393
Author(s):  
Yousri Slaoui
Keyword(s):  
Probability Density Function ◽  
Strong Consistency ◽  
Bandwidth Selection ◽  
Kernel Density ◽  
Kernel Estimator ◽  
Data Driven ◽  
Kernel Estimators ◽  
Convergence Properties ◽  
Selection For ◽  
Selection Of

AbstractIn this paper, we propose a data driven bandwidth selection of the recursive Gumbel kernel estimators of a probability density function based on a stochastic approximation algorithm. The choice of the bandwidth selection approaches is investigated by a second generation plug-in method. Convergence properties of the proposed recursive Gumbel kernel estimators are established. The uniform strong consistency of the proposed recursive Gumbel kernel estimators is derived. The new recursive Gumbel kernel estimators are compared to the non-recursive Gumbel kernel estimator and the performance of the two estimators are illustrated via simulations as well as a real application.

scholarly journals Data driven global weather predictions at high resolutions

2021 ◽  
Author(s):  
John Taylor ◽  
Pablo Larraonndo ◽  
Bronis de Supinski
Keyword(s):  
High Resolution ◽  
Graphics Processing Units ◽  
Weather Forecasting ◽  
Weather Prediction ◽  
Atmospheric Science ◽  
Data Driven ◽  
Research And Innovation ◽  
Future State ◽  
Graphics Processing ◽  
Quantities Of Interest

Abstract Society has benefited enormously from the continuous advancement in numerical weather prediction that has occurred over many decades driven by a combination of outstanding scientific, computational and technological breakthroughs. Here we demonstrate that data driven methods are now positioned to contribute to the next wave of major advances in atmospheric science. We show that data driven models can predict important meteorological quantities of interest to society such as global high resolution precipitation fields (0.25 degrees) and can deliver accurate forecasts of the future state of the atmosphere without prior knowledge of the laws of physics and chemistry. We also show how these data driven methods can be scaled to run on super-computers with up to 1024 modern graphics processing units (GPU) and beyond resulting in rapid training of data driven models, thus supporting a cycle of rapid research and innovation. Taken together, these two results illustrate the significant potential of data driven methods to advance atmospheric science and operational weather forecasting.

scholarly journals New Bandwidth Selection for Kernel Quantile Estimators

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Ali Al-Kenani ◽  
Keming Yu
Keyword(s):  
Cross Validation ◽  
Kernel Smoothing ◽  
Bandwidth Selection ◽  
Unbiased Estimation ◽  
Optimal Bandwidth ◽  
Squared Error ◽  
Bandwidth Parameter ◽  
Integrated Squared Error ◽  
Selection For ◽  
Quantile Estimators

We propose a cross-validation method suitable for smoothing of kernel quantile estimators. In particular, our proposed method selects the bandwidth parameter, which is known to play a crucial role in kernel smoothing, based on unbiased estimation of a mean integrated squared error curve of which the minimising value determines an optimal bandwidth. This method is shown to lead to asymptotically optimal bandwidth choice and we also provide some general theory on the performance of optimal, data-based methods of bandwidth choice. The numerical performances of the proposed methods are compared in simulations, and the new bandwidth selection is demonstrated to work very well.

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