×

Regularized least square regression with spherical polynomial kernels. (English) Zbl 1184.68410

Summary: This article considers regularized least square regression on the sphere. It develops a theoretical analysis of the generalization performances of regularized least square regression algorithm with spherical polynomial kernels. The explicit bounds are derived for the excess risk error. The learning rates depend on the eigenvalues of spherical polynomial integral operators and on the dimension of spherical polynomial spaces.

MSC:

68T05 Learning and adaptive systems in artificial intelligence
62J02 General nonlinear regression
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1090/S0002-9947-1950-0051437-7 · doi:10.1090/S0002-9947-1950-0051437-7
[2] DOI: 10.1142/S0219691308002379 · Zbl 1268.42052 · doi:10.1142/S0219691308002379
[3] DOI: 10.1080/00036817608839133 · Zbl 0341.41011 · doi:10.1080/00036817608839133
[4] Berens H., Publ. Res. Inst. Math. Sci. Ser. A 4 pp 168–
[5] DOI: 10.1007/BF03322314 · Zbl 0781.41011 · doi:10.1007/BF03322314
[6] Chen D. R., J. Mach. Learning Res. 5 pp 1143–
[7] DOI: 10.1142/S0219691309002970 · Zbl 1178.68400 · doi:10.1142/S0219691309002970
[8] DOI: 10.1007/s10496-007-0188-4 · Zbl 1141.68557 · doi:10.1007/s10496-007-0188-4
[9] DOI: 10.1007/s11425-007-0100-x · Zbl 1133.68393 · doi:10.1007/s11425-007-0100-x
[10] DOI: 10.1016/j.ins.2009.01.007 · Zbl 1192.68509 · doi:10.1016/j.ins.2009.01.007
[11] DOI: 10.1090/S0273-0979-01-00923-5 · Zbl 0983.68162 · doi:10.1090/S0273-0979-01-00923-5
[12] DOI: 10.1007/s102080010030 · Zbl 1057.68085 · doi:10.1007/s102080010030
[13] DOI: 10.1017/CBO9780511618796 · Zbl 1274.41001 · doi:10.1017/CBO9780511618796
[14] DOI: 10.1023/A:1018946025316 · Zbl 0939.68098 · doi:10.1023/A:1018946025316
[15] DOI: 10.1007/978-1-4612-0711-5 · doi:10.1007/978-1-4612-0711-5
[16] DOI: 10.1017/S095018430000029X · Zbl 0072.28401 · doi:10.1017/S095018430000029X
[17] DOI: 10.1007/BF03018264 · JFM 48.1243.03 · doi:10.1007/BF03018264
[18] DOI: 10.1142/S0219691308002409 · Zbl 1145.68494 · doi:10.1142/S0219691308002409
[19] Schölkopf B., Learning with Kernels (2002)
[20] DOI: 10.1016/j.jco.2008.05.008 · Zbl 1169.68043 · doi:10.1016/j.jco.2008.05.008
[21] de la Vallée-Poussin Ch. J., Bull. Acad. de. Belgique cl. Sci. 3 pp 193–
[22] Vapnik V., Statistical Learning Theory (1998) · Zbl 0935.62007
[23] DOI: 10.1007/s10208-004-0155-9 · Zbl 1100.68100 · doi:10.1007/s10208-004-0155-9
[24] DOI: 10.1162/0899766053491896 · Zbl 1108.90324 · doi:10.1162/0899766053491896
[25] Wang K. Y., Harmonic Analysis and Approximation on the Unit Sphere (2000)
[26] DOI: 10.1007/s10444-004-7206-2 · Zbl 1095.68103 · doi:10.1007/s10444-004-7206-2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.