Learning rates of regularized regression on the unit sphere 被引量：2

Learning rates of regularized regression on the unit sphere

导出

摘要 This paper addresses the learning algorithm on the unit sphere.The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel.The excess error can be estimated by the sum of sample errors and regularization errors.Our study shows that by introducing a suitable spherical harmonics kernel,the regularization parameter can decrease arbitrarily fast with the sample size. This paper addresses the learning algorithm on the unit sphere. The main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics kernel. The excess error can be estimated by the sum of sample errors and regularization errors. Our study shows that by introducing a suitable spherical harmonics kernel, the regularization parameter can decrease arbitrarily fast with the sample size.

作者 CAO FeiLong LIN ShaoBo CHANG XiangYu XU ZongBen

机构地区 Institute of Metrology and Computational Science Institute for Information and System Sciences

出处《Science China Mathematics》 SCIE 2013年第4期861-876,共16页 中国科学：数学（英文版）

基金 supported by National Natural Science Foundation of China (Grant Nos. 61272023 and 61075054)

关键词 SPHERE regularized regression spherical harmonics kernel rate of convergence 单位球面学习算法回归分析正规化最小二乘算法内核样本估计

分类号 O212.1 [理学—概率论与数理统计]

引文网络
相关文献

参考文献25

1Aronszajn N. Theory of reproducing kernels. Trans Amer Math Soc, 1950, 68:337 404.
2Belkin M, Niyogi P, Sindwani V. Manifold regularization: A geometric framework for learning from examples. Com- puter Science Technical Report of University of Chicago (TR-2004-06), 2004.
3Belkin M, Niyogi P. Semi-supervised learning on Riemannian manifolds. Machine Learning, 2004, 56:209 239.
4Chen D R, Wu Q, Ying Y M, et al. Support vector machine soft margin classifiers: Error analysis. J Mach Learning Res, 2004, 5:1143-1175.
5Cucker F, Smale S. On the mathematical foundations of learning. Bull Amer Math Soc, 2001, 39:1-49.
6Dai F. Jackson-type inequality for doubling weights on the sphere. Constr Approx, 2006, 24:91-112.
7Ditzian Z. A modulus of smoothness on the unit sphere. J Anal Math, 1999, 79:189-200.
8Ditzian Z. Jackson-type inequality on the sphere. Acta Math Hungar, 2004, 102:1-35.
9Freeden W, Gervens T, Schreiner M. Constructive Approximation on the Sphere. New York: Oxford University Press, 1998.
10Hubbert S, Morton T M. A Duchon framework for the sphere. J Approx Theory, 2004, 129:28-57.