3The Structural Risk Minimization principle on set-valued probability space

Author

Chen, Ji-qiang ; Ha, Ming-Hu ; Zheng, Li-fang

Author_Institution

Coll. of Sci., Hebei Univ. of Eng., Handan, China

Volume

4

fYear

2009

fDate

12-15 July 2009

Firstpage

1885

Lastpage

1890

Abstract

Statistical learning theory (SLT) based on random samples on probability space is considered as the best theory about small samples statistics learning at present and has become a new hot field in machine learning after neural networks. However, the theory can not handle the small samples statistical learning problems on set-valued probability space which widely exists in real world. In this paper, Borel-Cantelli lemma based on random sets is proven on set-valued probability space. The structural risk minimization (SRM) based on random sets samples on set-valued probability space is established.

Keywords

learning (artificial intelligence); probability; random sequences; set theory; statistical analysis; Borel-Cantelli lemma; machine learning; neural network; random set sequences; random set theory; set-valued probability space; statistical learning theory; structural risk minimization principle; Convergence; Cybernetics; Educational institutions; Extraterrestrial measurements; Machine learning; Probability; Random variables; Risk management; Statistical learning; Virtual colonoscopy; Random sets; Set-valued probability; The bounds on the rate of uniform convergence; The structural risk minimization principle;

fLanguage

English

Publisher

ieee

Conference_Titel

Machine Learning and Cybernetics, 2009 International Conference on

Conference_Location

Baoding

Print_ISBN

978-1-4244-3702-3

Electronic_ISBN

978-1-4244-3703-0

Type

conf

DOI

10.1109/ICMLC.2009.5212140

Filename

5212140