Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids
Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids
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dc.contributor.author | Bastian Bohn | |
dc.contributor.author | Michael Griebel | |
dc.contributor.author | Jens Oettershagen | |
dc.date.accessioned | 2024-08-13T12:17:43Z | |
dc.date.available | 2024-08-13T12:17:43Z | |
dc.date.issued | 02.2018 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/11825 | |
dc.description.abstract | For low-dimensional 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, grid-based discretizations of larger (kernel) model classes lead to algorithms, which naturally scale linearly in the amount of data points. For moderate-dimensional or high-dimensional regression tasks, these grid-based 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 dimension-adaptive sparse grids, which can detect and exploit a given low effective dimensionality of nominally high-dimensional data, are particularly successful. They nevertheless rely on an axis-aligned 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, problem-dependent 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 real-world data to show how an adaptive sparse grid least squares algorithm benefits from our preprocessing method. | en |
dc.format.extent | 21 | |
dc.language.iso | eng | |
dc.relation.ispartofseries | INS Preprints ; 1812 | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | effective dimensionality | |
dc.subject | ANOVA decomposition | |
dc.subject | adaptive sparse grids | |
dc.subject | least-squares regression | |
dc.subject.ddc | 510 Mathematik | |
dc.subject.ddc | 518 Numerische Analysis | |
dc.title | Optimally rotated coordinate systems for adaptive least-squares regression on sparse grids | |
dc.type | Preprint | |
dc.publisher.name | Institut für Numerische Simulation (INS) | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.relation.doi | https://doi.org/10.1137/1.9781611975673.19 | |
ulbbn.pubtype | Zweitveröffentlichung | |
dcterms.bibliographicCitation.url | https://ins.uni-bonn.de/publication/preprints |
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