On the convergence rate of sparse grid least squares regression
On the convergence rate of sparse grid least squares regression
View/Date of Publication
08.2017Publisher
Institut für Numerische Simulation (INS)Publisher Location
BonnMetadata
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Citable Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11833
Abstract
While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, error decay behavior and appropriate couplings between the dataset size and the grid size has not been provided yet.
In this paper, we will present a framework which will allow us to close this gap and rigorously derive upper bounds on the expected error for sparse grid least squares regression. Furthermore, we will verify that our theoretical convergence results also match the observed rates in numerical experiments.
In this paper, we will present a framework which will allow us to close this gap and rigorously derive upper bounds on the expected error for sparse grid least squares regression. Furthermore, we will verify that our theoretical convergence results also match the observed rates in numerical experiments.
Classification (DDC)
510 Mathematik 518 Numerische AnalysisFirst Publication
https://ins.uni-bonn.de/publication/preprintsRelated Publications
https://doi.org/10.1007/978-3-319-75426-0_2Part of Series
INS Preprints ; 1711Bohn, Bastian: On the convergence rate of sparse grid least squares regression. In: INS Preprints, 1711.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11833
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11833
@unpublished{handle:20.500.11811/11833,
author = {{Bastian Bohn}},
title = {On the convergence rate of sparse grid least squares regression},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = aug,
INS Preprints},
volume = 1711,
note = {While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, error decay behavior and appropriate couplings between the dataset size and the grid size has not been provided yet.
In this paper, we will present a framework which will allow us to close this gap and rigorously derive upper bounds on the expected error for sparse grid least squares regression. Furthermore, we will verify that our theoretical convergence results also match the observed rates in numerical experiments.},
url = {https://hdl.handle.net/20.500.11811/11833}
}
author = {{Bastian Bohn}},
title = {On the convergence rate of sparse grid least squares regression},
publisher = {Institut für Numerische Simulation (INS)},
year = 2017,
month = aug,
INS Preprints},
volume = 1711,
note = {While sparse grid least squares regression algorithms have been frequently used to tackle Big Data problems with a huge number of input data in the last 15 years, a thorough theoretical analysis of stability properties, error decay behavior and appropriate couplings between the dataset size and the grid size has not been provided yet.
In this paper, we will present a framework which will allow us to close this gap and rigorously derive upper bounds on the expected error for sparse grid least squares regression. Furthermore, we will verify that our theoretical convergence results also match the observed rates in numerical experiments.},
url = {https://hdl.handle.net/20.500.11811/11833}
}
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