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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Optimally rotated coordinate systems for adaptive leastsquares regression on sparse grids
 BergerWolf, T. ; Society for Industrial and Applied Mathematics SIAM, Philadelphia/Pa.: SIAM International Conference on Data Mining 2019. Proceedings : May 24, 2019, Calgary, Canada Philadelphia: SIAM, 2019 ISBN: 9781611975673 S.163171 
 International Conference on Data Mining <2019, Calgary> 
 Deutsche Forschungsgemeinschaft DFG SFB 1060; 211504053 

 Englisch 
 Konferenzbeitrag 
 Fraunhofer SCAI () 
Abstract
For lowdimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, gridbased discretizations of larger (kernel) model classes lead to algorithms, which naturally scale linearly in the amount of data points. For moderatedimensional or highdimensional regression tasks, these gridbased discretizations suffer from the curse of dimensionality. Here, sparse grid methods have proven to circumvent this problem to a large extent. In this context, space and dimensionadaptive sparse grids, which can detect and exploit a given low effective dimensionality of nominally highdimensional data, are particularly successful. They nevertheless rely on an axisaligned structure of the solution and exhibit issues for data with predominantly skewed and rotated coordinates.
In this paper we propose a preprocessing approach for these adaptive sparse grid algorithms that determines an optimized, problemdependent coordinate system and, thus, reduces the effective dimensionality of a given data set in the ANOVA sense. We provide numerical examples on synthetic data as well as realworld data to show how an adaptive sparse grid least squares algorithm benefits from our preprocessing method.