Title :
A Further Discussion on Bounds on the Rate of Uniform Convergence of Learning Theory Based on Fuzzy Samples
Author :
Chen, Ji-qiang ; Ha, Ming-Hu
Author_Institution :
Coll. of Sci., Hebei Univ. of Eng., Handan, China
Abstract :
Statistical Learning Theory (SLT) based on random samples formed in probability space is considered at present as one of the fundamental theories about small samples statistical learning. It has become a novel and important field of machine learning along with other concepts and architectures such as neural networks. However, many problems involve fuzzy samples in real word and the theory hardly handles statistical learning problems for them. Being motivated by some applications and the ambiguity of real world, in this study, we further develop an SLT based on fuzzy samples. Firstly, we prove a certain law of Hoeffding inequality for fuzzy random variables. Secondly, we further present the bounds on the rate of uniform convergence of learning theory based on fuzzy samples in probability space, which become cornerstones of the theoretical fundamentals of the SLT for fuzzy samples.
Keywords :
fuzzy set theory; learning (artificial intelligence); probability; statistical analysis; Hoeffding inequality; fuzzy random variables; fuzzy samples; machine learning; neural networks; probability space; random samples; statistical learning theory; uniform convergence; Convergence; Fuzzy systems; Intelligent systems; Machine learning; Mathematics; Neural networks; Probability; Random variables; Statistical learning; Support vector machines; Fuzzy numbers; bounds on the rate of uniform convergence; fuzzy random variable; probability; the key theorem;
Conference_Titel :
Intelligent Systems, 2009. GCIS '09. WRI Global Congress on
Conference_Location :
Xiamen
Print_ISBN :
978-0-7695-3571-5
DOI :
10.1109/GCIS.2009.412