Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/88214
DC Field | Value | Language |
---|---|---|
dc.contributor | Department of Applied Mathematics | en_US |
dc.creator | Guo, X | en_US |
dc.creator | Lin, J | en_US |
dc.creator | Zhou, DX | en_US |
dc.date.accessioned | 2020-09-24T02:33:40Z | - |
dc.date.available | 2020-09-24T02:33:40Z | - |
dc.identifier.uri | http://hdl.handle.net/10397/88214 | - |
dc.language.iso | en | en_US |
dc.rights | Posted with permission of the author. | en_US |
dc.title | Convergence of the randomized kaczmarz algorithm in Hilbert space | en_US |
dc.type | Presentation | en_US |
dcterms.abstract | The randomized Kaczmarz algorithm recently draws much attention. Existing results on anal-ysis suffer from condition numbers of the linear equation systems. Although the randomized Kacz-marz algorithm has a natural generalization to Hilbert spaces (which covers online learning algo-rithms for a particular instance), the existing analysis does not. Although the large-scale linear equation system is an ideal scenario for the randomized Kaczmarz algorithm to outperform direct solvers, it is also a scenario the existing analysis is not satisfactory. In this research, we introduce the regularity assumption widely adopted in learning theory and obtain the polynomial convergence rate of the randomized Kaczmarz algorithm in Hilbert space under noise-free setting. We find that by nature, the randomized Kaczmarz algorithm converges weakly. Meanwhile, with noisy data, we study the relaxation method and obtain a strong convergence arbitrarily close to the minimax optimal rate. The result applies to online gradient descent learning algorithms and significantly improves the existing learning rate in literature. | en_US |
dcterms.accessRights | open access | en_US |
dcterms.bibliographicCitation | Paper presented at International Conference on Computational Harmonic Analysis 2017, Shanghai, China, 24-28 May 2017 | en_US |
dcterms.issued | 2017-05-27 | - |
dc.relation.conference | International Conference on Computational Harmonic Analysis | en_US |
dc.description.validate | 202009 bcwh | en_US |
dc.description.oa | Not applicable | en_US |
dc.identifier.FolderNumber | a0481-n11 | - |
dc.description.oaCategory | Copyright retained by author | en_US |
Appears in Collections: | Presentation |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
FudanShanghai2017May.pdf | 93.13 kB | Adobe PDF | View/Open |
Page views
139
Last Week
0
0
Last month
Citations as of Dec 8, 2024
Downloads
57
Citations as of Dec 8, 2024
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.