Error estimates for multivariate regression on discretized function spaces
Error estimates for multivariate regression on discretized function spaces
Dokument öffnen (326.6KB)Datum der Veröffentlichung
03.2016Verlag / herausgebende Einrichtung
Institut für Numerische Simulation (INS)Verlagsort
BonnMetadaten
Zur Langanzeige
Zitierbarer Link (Handle URI) 
https://hdl.handle.net/20.500.11811/11918
Inhalt
In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling error and the discretization error interact and how they can be balanced appropriately. We will present two examples based on tensor product spaces (sparse grids, hyperbolic crosses) which provide a suitable approach in the case of large sample sets in moderate dimensions.
Schlagwörter
regression, learning theory, convergence rates, discretized function spaces, sparse grids, bias-variance problem
Klassifikation (DDC)
510 Mathematik 518 Numerische AnalysisErstpublikation
https://ins.uni-bonn.de/publication/preprintsZugehörige Publikation(en)
https://doi.org/10.1137/15M1013973Reihe, Nummer
INS Preprints ; 1412Bohn, Bastian; Griebel, Michael: Error estimates for multivariate regression on discretized function spaces. In: INS Preprints, 1412.
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11918
Online-Ausgabe in bonndoc: https://hdl.handle.net/20.500.11811/11918
@unpublished{handle:20.500.11811/11918,
author = {{Bastian Bohn} and {Michael Griebel}},
title = {Error estimates for multivariate regression on discretized function spaces},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = mar,
INS Preprints},
volume = 1412,
note = {In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling error and the discretization error interact and how they can be balanced appropriately. We will present two examples based on tensor product spaces (sparse grids, hyperbolic crosses) which provide a suitable approach in the case of large sample sets in moderate dimensions.},
url = {https://hdl.handle.net/20.500.11811/11918}
}
author = {{Bastian Bohn} and {Michael Griebel}},
title = {Error estimates for multivariate regression on discretized function spaces},
publisher = {Institut für Numerische Simulation (INS)},
year = 2016,
month = mar,
INS Preprints},
volume = 1412,
note = {In this paper, we will discuss the discretization error for the regression setting and derive error bounds relying on the approximation properties of the discretized space. Furthermore, we will point out how the sampling error and the discretization error interact and how they can be balanced appropriately. We will present two examples based on tensor product spaces (sparse grids, hyperbolic crosses) which provide a suitable approach in the case of large sample sets in moderate dimensions.},
url = {https://hdl.handle.net/20.500.11811/11918}
}
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