Adaptive parameter selection for kernel ridge regression
This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR estimates. Based on this observation, we develop an early-stoppi...
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| Published in | Applied and computational harmonic analysis Vol. 73; p. 101671 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
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01.11.2024
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| Abstract | This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR estimates. Based on this observation, we develop an early-stopping type parameter selection strategy for KRR according to the so-called Lepskii-type principle. Theoretical verifications are presented in the framework of learning theory to show that KRR equipped with the proposed parameter selection strategy succeeds in achieving optimal learning rates and adapts to different norms, providing a new record of parameter selection for kernel methods. |
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| AbstractList | This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR estimates. Based on this observation, we develop an early-stopping type parameter selection strategy for KRR according to the so-called Lepskii-type principle. Theoretical verifications are presented in the framework of learning theory to show that KRR equipped with the proposed parameter selection strategy succeeds in achieving optimal learning rates and adapts to different norms, providing a new record of parameter selection for kernel methods. |
| ArticleNumber | 101671 |
| Author | Lin, Shao-Bo |
| Author_xml | – sequence: 1 givenname: Shao-Bo surname: Lin fullname: Lin, Shao-Bo email: sblin1983@gmail.com organization: Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi'an Jiaotong University, Xi'an 710049, China |
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| References | De Vito, Pereverzyev, Rosasco (br0170) 2010; 10 Lin, Wang, Zhou (br0320) 2020; 21 Lepskii (br0160) 1991; 35 Blanchard, Mathé, Mücke (br0130) 2019 Raskutti, Wainwright, Yu (br0300) 2014; 15 Smale, Zhou (br0180) 2005; 19 Gerfo, Rosasco, Odone, Vito, Verri (br0060) 2008; 20 Christmann, Xiang, Zhou (br0080) 2018; 289 Celisse, Wahl (br0110) 2021; 22 Bhatia (br0330) 2013 Engl, Hanke, Neubauer (br0150) 1996 Lu, Mathé, Pereverzyev (br0270) 2019; 17 Köhler, Christmann (br0090) 2022; 23 Blanchard, Mücke (br0240) 2018; 18 Lin, Lei, Zhou (br0050) 2019; 20 Lu, Mathé, Pereverzev (br0120) 2020; 48 Smale, Zhou (br0310) 2004; 41 Caponnetto, De Vito (br0010) 2007; 7 Steinwart, Christmann (br0230) 2008 Blanchard, Krämer (br0260) 2016; 14 Smale, Zhou (br0190) 2007; 26 Cucker, Smale (br0070) 2002; 2 Fischer, Steinwart (br0280) 2020; 21 Caponnetto, Yao (br0100) 2010; 8 Guo, Lin, Zhou (br0290) 2017; 33 Steinwart, Hush, Scovel (br0200) 2009 Meister, Steinwart (br0040) 2016; 17 Györfi, Kohler, Krzyżak, Walk (br0140) 2002 Rudi, Camoriano, Rosasco (br0020) 2015 Lin, Guo, Zhou (br0210) 2017; 18 Chang, Lin, Zhou (br0250) 2017; 18 Zhang, Duchi, Wainwright (br0030) 2015; 16 Cucker, Zhou (br0220) 2007 Blanchard (10.1016/j.acha.2024.101671_br0130) Raskutti (10.1016/j.acha.2024.101671_br0300) 2014; 15 Cucker (10.1016/j.acha.2024.101671_br0070) 2002; 2 Smale (10.1016/j.acha.2024.101671_br0180) 2005; 19 Caponnetto (10.1016/j.acha.2024.101671_br0010) 2007; 7 De Vito (10.1016/j.acha.2024.101671_br0170) 2010; 10 Lin (10.1016/j.acha.2024.101671_br0050) 2019; 20 Lu (10.1016/j.acha.2024.101671_br0120) 2020; 48 Köhler (10.1016/j.acha.2024.101671_br0090) 2022; 23 Bhatia (10.1016/j.acha.2024.101671_br0330) 2013 Smale (10.1016/j.acha.2024.101671_br0190) 2007; 26 Györfi (10.1016/j.acha.2024.101671_br0140) 2002 Lin (10.1016/j.acha.2024.101671_br0320) 2020; 21 Lepskii (10.1016/j.acha.2024.101671_br0160) 1991; 35 Gerfo (10.1016/j.acha.2024.101671_br0060) 2008; 20 Caponnetto (10.1016/j.acha.2024.101671_br0100) 2010; 8 Meister (10.1016/j.acha.2024.101671_br0040) 2016; 17 Smale (10.1016/j.acha.2024.101671_br0310) 2004; 41 Fischer (10.1016/j.acha.2024.101671_br0280) 2020; 21 Rudi (10.1016/j.acha.2024.101671_br0020) 2015 Engl (10.1016/j.acha.2024.101671_br0150) 1996 Cucker (10.1016/j.acha.2024.101671_br0220) 2007 Celisse (10.1016/j.acha.2024.101671_br0110) 2021; 22 Steinwart (10.1016/j.acha.2024.101671_br0200) 2009 Lu (10.1016/j.acha.2024.101671_br0270) 2019; 17 Lin (10.1016/j.acha.2024.101671_br0210) 2017; 18 Zhang (10.1016/j.acha.2024.101671_br0030) 2015; 16 Steinwart (10.1016/j.acha.2024.101671_br0230) 2008 Blanchard (10.1016/j.acha.2024.101671_br0240) 2018; 18 Blanchard (10.1016/j.acha.2024.101671_br0260) 2016; 14 Christmann (10.1016/j.acha.2024.101671_br0080) 2018; 289 Chang (10.1016/j.acha.2024.101671_br0250) 2017; 18 Guo (10.1016/j.acha.2024.101671_br0290) 2017; 33 |
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