Error analysis of regularized and unregularized least-squares regression on discretized function spaces
Error analysis of regularized and unregularized least-squares regression on discretized function spaces
dc.contributor.advisor | Griebel, Michael | |
dc.contributor.author | Bohn, Bastian | |
dc.date.accessioned | 2020-04-23T18:06:05Z | |
dc.date.available | 2020-04-23T18:06:05Z | |
dc.date.issued | 04.01.2017 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/7094 | |
dc.description.abstract | In this thesis, we analyze a variant of the least-squares regression method which operates on subsets of finite-dimensional vector spaces. In the first part, we focus on a regression problem which is constrained to a ball of finite radius in the search space. We derive an upper bound on the overall error by coupling the ball radius to the resolution of the search space. In the second part, the corresponding penalized Lagrangian dual problem is considered to establish probabilistic results on the well-posedness of the underlying minimization problem. Furthermore, we have a look at the limit case, where the penalty term vanishes and we improve on our error estimates from the first part for the special case of noiseless function reconstruction. Subsequently, our theoretical foundation is used to obtain novel convergence results for regression algorithms based on sparse grids with linear splines and Fourier polynomial spaces on hyperbolic crosses. We conclude the thesis by giving several numerical examples and comparing the observed error behavior to our theoretical results. | |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject | Big Data | |
dc.subject | Regressionsanalyse | |
dc.subject | Maschinelles Lernen | |
dc.subject | Kleinste-Quadrate-Methode | |
dc.subject | Dünnes Gitter | |
dc.subject | Regression analysis | |
dc.subject | Machine Learning | |
dc.subject | Least squares method | |
dc.subject | Sparse grid | |
dc.subject.ddc | 510 Mathematik | |
dc.title | Error analysis of regularized and unregularized least-squares regression on discretized function spaces | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5n-45798 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 4579 | |
ulbbnediss.date.accepted | 09.12.2016 | |
ulbbnediss.institute | Mathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Institut für Numerische Simulation (INS) | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Garcke, Jochen |
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