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Leave-one-out bounds for kernel methods. (English) Zbl 1085.68144

Summary: In this article, we study leave-one-out style cross-validation bounds for kernel methods. The essential element in our analysis is a bound on the parameter estimation stability for regularized kernel formulations. Using this result, we derive bounds on expected leave-one-out cross-validation errors, which lead to expected generalization bounds for various kernel algorithms. In addition, we also obtain variance bounds for leave-oneout errors. We apply our analysis to some classification and regression problems and compare them with previous results.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
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[1] DOI: 10.1007/BF01199316 · Zbl 0805.62037 · doi:10.1007/BF01199316
[2] DOI: 10.1162/153244302760200704 · Zbl 1007.68083 · doi:10.1162/153244302760200704
[3] DOI: 10.1090/S0273-0979-01-00923-5 · Zbl 0983.68162 · doi:10.1090/S0273-0979-01-00923-5
[4] DOI: 10.1214/aos/1176345462 · Zbl 0481.62035 · doi:10.1214/aos/1176345462
[5] DOI: 10.1023/A:1018946025316 · Zbl 0939.68098 · doi:10.1023/A:1018946025316
[6] DOI: 10.1162/089976699300016304 · doi:10.1162/089976699300016304
[7] DOI: 10.1023/A:1018967708053 · Zbl 0939.41012 · doi:10.1023/A:1018967708053
[8] DOI: 10.1023/A:1018996230401 · Zbl 0907.65006 · doi:10.1023/A:1018996230401
[9] DOI: 10.1214/aos/1176349952 · Zbl 0604.62017 · doi:10.1214/aos/1176349952
[10] DOI: 10.1006/jath.1997.3137 · Zbl 0904.41013 · doi:10.1006/jath.1997.3137
[11] DOI: 10.1214/aos/1017939142 · Zbl 0978.62008 · doi:10.1214/aos/1017939142
[12] DOI: 10.1023/A:1012498226479 · Zbl 0998.68100 · doi:10.1023/A:1012498226479
[13] Zhang T., Annals of Statitics.
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