Analysis of Support Vector Machines Regression

Authors:
Hongzhi Tong;Di-Rong Chen;Lizhong Peng
Affiliations:
Peking University, LMAM, School of Mathematical Sciences, 100871, Beijing, People’s Republic of China;Beijing University of Aeronautics and Astronautics, Department of Mathematics, and LMIB, 100083, Beijing, People’s Republic of China;Peking University, LMAM, School of Mathematical Sciences, 100871, Beijing, People’s Republic of China
Venue:
Foundations of Computational Mathematics
Year:
2009

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Abstract

Support vector machines regression (SVMR) is a regularized learning algorithm in reproducing kernel Hilbert spaces with a loss function called the ε-insensitive loss function. Compared with the well-understood least square regression, the study of SVMR is not satisfactory, especially the quantitative estimates of the convergence of this algorithm. This paper provides an error analysis for SVMR, and introduces some recently developed methods for analysis of classification algorithms such as the projection operator and the iteration technique. The main result is an explicit learning rate for the SVMR algorithm under some assumptions.