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Generalized kernel regression estimatefor the identification of Hammerstein systems

100%

Mzyk G.

International Journal of Applied Mathematics and Computer Science

2007

tom 17

nr 2

189-197

A modified version of the classical kernel nonparametric identification algorithm for nonlinearity recovering in a Hammerstein system under the existence of random noise is proposed. The assumptions imposed on the unknown characteristic are weak. The generalized kernel method proposed in the paper provides more accurate results in comparison with the classical kernel nonparametric estimate, regardless of the number of measurements. The convergence in probability of the proposed estimate to the unknown characteristic is proved and the question of the convergence rate is discussed. Illustrative simulation examples are included.

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

88%

Andrzejewski W., Gramacki A., Gramacki J.

International Journal of Applied Mathematics and Computer Science

2013

tom 23

nr 4

869-885

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.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Andrzejewski W.

1 Gramacki A.

1 Gramacki J.

1 Mzyk G.

1 2013

1 2007

Wyniki wyszukiwania

Generalized kernel regression estimatefor the identification of Hammerstein systems

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