Research Article
Open Access
Exponential Inequality for the Dependent V-statistics of Bivariate Affine Functions
1
College of Informatics, Huazhong Agricultural University, Wuhan 430070, China
* Corresponding Author:
Liyuan Liu,
[email protected]
Volume 1, Issue 2
2025
Received: 04 September 2025
Accepted: 15 September 2025
Published: 18 September 2025
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CC BY 4.0 License
Article Information
Volume/Issue
Volume 1, Issue 2, 2025
Pages
54-59
Abstract
Binary functions have a wide range of applications in the fields of machine learning, statistical learning, and so on. In this paper, we investigate the exponential inequalities for the independent $V$-statistics of binary affine functions and obtain a universal inequality for $V$-statistics. Due to the typical characteristics of this kind of binary function, including symmetry and affinity, this work has great practical significance. Finally, we derive the corresponding inequalities in the context of specific similarity learning.
Keywords
$V$-statistics
symmetric binary affine function
exponential inequality
similarity learning
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
References
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APA Style
Zhou, R., Li, W., & Liu, L. (2025). Exponential Inequality for the Dependent V-statistics of Bivariate Affine Functions. Journal of Numerical Simulations in Physics and Mathematics, 1(2), 54–59. https://doi.org/10.62762/JNSPM.2025.502885
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TY - JOUR AU - Zhou, Richeng AU - Li, Weifu AU - Liu, Liyuan PY - 2025 DA - 2025/09/18 TI - Exponential Inequality for the Dependent V-statistics of Bivariate Affine Functions JO - Journal of Numerical Simulations in Physics and Mathematics T2 - Journal of Numerical Simulations in Physics and Mathematics JF - Journal of Numerical Simulations in Physics and Mathematics VL - 1 IS - 2 SP - 54 EP - 59 DO - 10.62762/JNSPM.2025.502885 UR - https://www.icck.org/article/abs/JNSPM.2025.502885 KW - $V$-statistics KW - symmetric binary affine function KW - exponential inequality KW - similarity learning AB - Binary functions have a wide range of applications in the fields of machine learning, statistical learning, and so on. In this paper, we investigate the exponential inequalities for the independent $V$-statistics of binary affine functions and obtain a universal inequality for $V$-statistics. Due to the typical characteristics of this kind of binary function, including symmetry and affinity, this work has great practical significance. Finally, we derive the corresponding inequalities in the context of specific similarity learning. SN - 3068-9082 PB - Institute of Central Computation and Knowledge LA - English ER -
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Compatible with LaTeX, BibTeX, and other reference managers
@article{Zhou2025Exponentia,
author = {Richeng Zhou and Weifu Li and Liyuan Liu},
title = {Exponential Inequality for the Dependent V-statistics of Bivariate Affine Functions},
journal = {Journal of Numerical Simulations in Physics and Mathematics},
year = {2025},
volume = {1},
number = {2},
pages = {54-59},
doi = {10.62762/JNSPM.2025.502885},
url = {https://www.icck.org/article/abs/JNSPM.2025.502885},
abstract = {Binary functions have a wide range of applications in the fields of machine learning, statistical learning, and so on. In this paper, we investigate the exponential inequalities for the independent \$V\$-statistics of binary affine functions and obtain a universal inequality for \$V\$-statistics. Due to the typical characteristics of this kind of binary function, including symmetry and affinity, this work has great practical significance. Finally, we derive the corresponding inequalities in the context of specific similarity learning.},
keywords = {\$V\$-statistics, symmetric binary affine function, exponential inequality, similarity learning},
issn = {3068-9082},
publisher = {Institute of Central Computation and Knowledge}
}
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