Optimal learning rates for least squares regularized regression with unbounded sampling
Cheng Wang
1
,
Ding-Xuan Zhou
2
Publication type: Journal Article
Publication date: 2011-02-01
scimago Q1
wos Q1
SJR: 0.850
CiteScore: 3.5
Impact factor: 1.8
ISSN: 0885064X, 10902708
General Mathematics
Statistics and Probability
Applied Mathematics
Control and Optimization
Numerical Analysis
Algebra and Number Theory
Abstract
A standard assumption in theoretical study of learning algorithms for regression is uniform boundedness of output sample values. This excludes the common case with Gaussian noise. In this paper we investigate the learning algorithm for regression generated by the least squares regularization scheme in reproducing kernel Hilbert spaces without the assumption of uniform boundedness for sampling. By imposing some incremental conditions on moments of the output variable, we derive learning rates in terms of regularity of the regression function and capacity of the hypothesis space. The novelty of our analysis is a new covering number argument for bounding the sample error.
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49
Total citations:
49
Citations from 2024:
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(14.28%)
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GOST
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Wang C., Zhou D. Optimal learning rates for least squares regularized regression with unbounded sampling // Journal of Complexity. 2011. Vol. 27. No. 1. pp. 55-67.
GOST all authors (up to 50)
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Wang C., Zhou D. Optimal learning rates for least squares regularized regression with unbounded sampling // Journal of Complexity. 2011. Vol. 27. No. 1. pp. 55-67.
Cite this
RIS
Copy
TY - JOUR
DO - 10.1016/j.jco.2010.10.002
UR - https://doi.org/10.1016/j.jco.2010.10.002
TI - Optimal learning rates for least squares regularized regression with unbounded sampling
T2 - Journal of Complexity
AU - Wang, Cheng
AU - Zhou, Ding-Xuan
PY - 2011
DA - 2011/02/01
PB - Elsevier
SP - 55-67
IS - 1
VL - 27
SN - 0885-064X
SN - 1090-2708
ER -
Cite this
BibTex (up to 50 authors)
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@article{2011_Wang,
author = {Cheng Wang and Ding-Xuan Zhou},
title = {Optimal learning rates for least squares regularized regression with unbounded sampling},
journal = {Journal of Complexity},
year = {2011},
volume = {27},
publisher = {Elsevier},
month = {feb},
url = {https://doi.org/10.1016/j.jco.2010.10.002},
number = {1},
pages = {55--67},
doi = {10.1016/j.jco.2010.10.002}
}
Cite this
MLA
Copy
Wang, Cheng, and Ding-Xuan Zhou. “Optimal learning rates for least squares regularized regression with unbounded sampling.” Journal of Complexity, vol. 27, no. 1, Feb. 2011, pp. 55-67. https://doi.org/10.1016/j.jco.2010.10.002.