×

Half supervised coefficient regularization for regression learning with unbounded sampling. (English) Zbl 1333.68228

The authors study a coefficient-based regularization scheme for least squares regression in a hypothesis space generated by a set of unlabeled data. Error analysis is carried out by estimating hypothesis error, sample error, and approximation error by an integral operator approach. Learning rates are derived when a moment hypothesis is satisfied for the unbounded sampling process and the regression function lies in the range of a power of an integral operator.

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: 10.1016/j.jco.2006.07.001 · Zbl 1109.68088 · doi:10.1016/j.jco.2006.07.001
[3] DOI: 10.1007/s10208-006-0196-8 · Zbl 1129.68058 · doi:10.1007/s10208-006-0196-8
[4] DOI: 10.1090/S0273-0979-01-00923-5 · Zbl 0983.68162 · doi:10.1090/S0273-0979-01-00923-5
[5] DOI: 10.1016/j.jco.2009.01.002 · Zbl 1319.62087 · doi:10.1016/j.jco.2009.01.002
[6] DOI: 10.1023/A:1018946025316 · Zbl 0939.68098 · doi:10.1023/A:1018946025316
[7] DOI: 10.1007/s10287-008-0072-5 · Zbl 1280.62074 · doi:10.1007/s10287-008-0072-5
[8] Guo Z. C., Adv. Comput. Math.
[9] DOI: 10.1109/TPAMI.2005.78 · Zbl 05111097 · doi:10.1109/TPAMI.2005.78
[10] DOI: 10.1214/009053606000001082 · doi:10.1214/009053606000001082
[11] DOI: 10.1162/neco.2008.05-07-517 · Zbl 1147.68643 · doi:10.1162/neco.2008.05-07-517
[12] DOI: 10.1007/s11785-011-0139-0 · Zbl 1285.68143 · doi:10.1007/s11785-011-0139-0
[13] Mairal J., J. Mach. Learn. Res. 11 pp 19– (2010)
[14] Poggio T., Notices Amer. Math. Soc. 50 pp 537– (2003)
[15] Sheng B. H., J. Comput. 4 pp 671– (2011)
[16] DOI: 10.1016/j.acha.2011.01.001 · Zbl 1221.68201 · doi:10.1016/j.acha.2011.01.001
[17] DOI: 10.1007/s00365-006-0659-y · Zbl 1127.68088 · doi:10.1007/s00365-006-0659-y
[18] DOI: 10.1080/00207160.2011.587511 · Zbl 1237.68165 · doi:10.1080/00207160.2011.587511
[19] DOI: 10.1016/j.mcm.2008.08.005 · Zbl 1165.45310 · doi:10.1016/j.mcm.2008.08.005
[20] DOI: 10.1016/j.acha.2010.04.001 · Zbl 1225.65015 · doi:10.1016/j.acha.2010.04.001
[21] Vapnik V., Statistical Learning Theory (1998) · Zbl 0935.62007
[22] Vapnik V., Autom. Remote Control. 10 (3) pp 1495– (1977)
[23] DOI: 10.1007/s10114-012-9739-5 · Zbl 1258.68072 · doi:10.1007/s10114-012-9739-5
[24] DOI: 10.1016/j.jco.2010.10.002 · Zbl 1217.65024 · doi:10.1016/j.jco.2010.10.002
[25] DOI: 10.1162/0899766053491896 · Zbl 1108.90324 · doi:10.1162/0899766053491896
[26] DOI: 10.1016/j.camwa.2008.09.014 · Zbl 1165.68388 · doi:10.1016/j.camwa.2008.09.014
[27] DOI: 10.1007/s10208-004-0155-9 · Zbl 1100.68100 · doi:10.1007/s10208-004-0155-9
[28] Ying, Y., Campbell, C. and Girolami, M.Analysis of SVM with indefinite kernels. Conference of Advances in Neural Information Processing Systems. Vol. 22, Available athttp://books.nips.cc/papers/files/nips22/NIPS2009_0135.pdf.
[29] DOI: 10.1162/089976603321780326 · Zbl 1085.68144 · doi:10.1162/089976603321780326
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.