Title :
A Relationship Between Generalization Error and Training Samples in Kernel Regressors
Author :
Tanaka, Akira ; Imai, Hideyuki ; Kudo, Mineichi ; Miyakoshi, Masaaki
Author_Institution :
Div. of Comput. Sci., Hokkaido Univ., Sapporo, Japan
Abstract :
A relationship between generalization error and training samples in kernel regressors is discussed in this paper. The generalization error can be decomposed into two components. One is a distance between an unknown true function and an adopted model space. The other is a distance between an estimated function and the orthogonal projection of the unknown true function onto the model space. In our previous work, we gave a framework to evaluate the first component. In this paper, we theoretically analyze the second one and show that a larger set of training samples usually causes a larger generalization error.
Keywords :
Hilbert spaces; generalisation (artificial intelligence); learning (artificial intelligence); regression analysis; adopted model space; estimated function; generalization error; kernel regressors; training samples; unknown true function; Analytical models; Hafnium; Hilbert space; Kernel; Noise; Training; Training data; generalization error; kernel regressor; reproducing kernel Hilbert space; sample points;
Conference_Titel :
Pattern Recognition (ICPR), 2010 20th International Conference on
Conference_Location :
Istanbul
Print_ISBN :
978-1-4244-7542-1
DOI :
10.1109/ICPR.2010.351