We analyze the learning rates for the least square regression with data dependent hy- pothesis spaces and coefficient regularization algorithms based on general kernels. Under a very mild regularity condition on the r...We analyze the learning rates for the least square regression with data dependent hy- pothesis spaces and coefficient regularization algorithms based on general kernels. Under a very mild regularity condition on the regression function, we obtain a bound for the approximation error by esti- mating the corresponding K：-functional. Combining this estimate with the previous result of the sample error, we derive a dimensional free learning rate by the proper choice of the regularization parameter.展开更多
基金Supported by National Natural Science Foundation of China (Grant Nos. 10871226, 10971251)Natural Science Foundation of Zhejiang Province (Grant No. Y6100096)supported by Program for New Century Excellent Talents in University
文摘We analyze the learning rates for the least square regression with data dependent hy- pothesis spaces and coefficient regularization algorithms based on general kernels. Under a very mild regularity condition on the regression function, we obtain a bound for the approximation error by esti- mating the corresponding K：-functional. Combining this estimate with the previous result of the sample error, we derive a dimensional free learning rate by the proper choice of the regularization parameter.
