Structural Risk Minimization Principle Based on Complex Fuzzy Random Samples
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@Article{JICS-5-019,
author = {Zhiming Zhang, Jingfeng Tian},
title = {Structural Risk Minimization Principle Based on Complex Fuzzy Random Samples},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {5},
number = {1},
pages = {019--040},
abstract = { Statistical Learning Theory is commonly regarded as a sound framework within which we
handle a variety of learning problems in presence of small size data samples. It has become a rapidly
progressing research area in machine learning. The theory is based on real random samples and as such is not
ready to deal with the statistical learning problems involving complex fuzzy random samples, which we may
encounter in real world scenarios. This paper explores statistical learning theory based on complex fuzzy
random samples. Firstly, the definition of complex fuzzy random variable is introduced. Next the concepts
and some properties of the mathematical expectation and independence of complex fuzzy random variables
are provided. Secondly, the concepts of annealed entropy, growth function and VC dimension of measurable
complex fuzzy set valued functions are proposed, and the bounds on the rate of uniform convergence of
learning process based on complex fuzzy random samples are constructed. Thirdly, on the basis of these
bounds, the idea of the complex fuzzy structural risk minimization principle is presented. Finally, the
consistency of this principle is proven and the bound on the asymptotic rate of convergence is derived.
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22726.html}
}
TY - JOUR
T1 - Structural Risk Minimization Principle Based on Complex Fuzzy Random Samples
AU - Zhiming Zhang, Jingfeng Tian
JO - Journal of Information and Computing Science
VL - 1
SP - 019
EP - 040
PY - 2024
DA - 2024/01
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22726.html
KW - complex fuzzy random variable, annealed entropy, growth function, VC dimension, complex
fuzzy structural risk minimization principle, bound on the asymptotic rate of convergence
AB - Statistical Learning Theory is commonly regarded as a sound framework within which we
handle a variety of learning problems in presence of small size data samples. It has become a rapidly
progressing research area in machine learning. The theory is based on real random samples and as such is not
ready to deal with the statistical learning problems involving complex fuzzy random samples, which we may
encounter in real world scenarios. This paper explores statistical learning theory based on complex fuzzy
random samples. Firstly, the definition of complex fuzzy random variable is introduced. Next the concepts
and some properties of the mathematical expectation and independence of complex fuzzy random variables
are provided. Secondly, the concepts of annealed entropy, growth function and VC dimension of measurable
complex fuzzy set valued functions are proposed, and the bounds on the rate of uniform convergence of
learning process based on complex fuzzy random samples are constructed. Thirdly, on the basis of these
bounds, the idea of the complex fuzzy structural risk minimization principle is presented. Finally, the
consistency of this principle is proven and the bound on the asymptotic rate of convergence is derived.
Zhiming Zhang, Jingfeng Tian. (2024). Structural Risk Minimization Principle Based on Complex Fuzzy Random Samples.
Journal of Information and Computing Science. 5 (1).
019-040.
doi:
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