Title :
The key theorem of statistical learning theory on possibility spaces
Author :
Bai, Yun-Chao ; Ha, Ming-Hu
Author_Institution :
Coll. of Econ., Hebei Univ., Baoding, China
Abstract :
In this paper, we will further discuss the property of the credibility measure and give Tchebycheff´s inequality and a large number theorem. On possibility measure spaces, we will give some new concepts of the empirical risk functional, the expected risk functional and the empirical risk minimization inductive principle (ERM) according to the classical statistical learning theory. At last, we will give and prove the key theorem of the statistical learning on possibility measure spaces.
Keywords :
learning (artificial intelligence); minimisation; minimum principle; possibility theory; risk analysis; statistical analysis; Tchebycheff inequality; credibility measure; possibility measure space; risk functional; risk minimization inductive principle; statistical learning theory; Additives; Chromium; Educational institutions; Extraterrestrial measurements; Machine learning; National electric code; Power measurement; Probability; Risk management; Statistical learning; Credibility measure; the empirical risk functional; the empirical risk minimization of principle; the expected risk functional; the key theorem;
Conference_Titel :
Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on
Conference_Location :
Guangzhou, China
Print_ISBN :
0-7803-9091-1
DOI :
10.1109/ICMLC.2005.1527708
