Exponential Inequality for the Dependent V-statistics of Bivariate Affine Functions

Richeng Zhou; Weifu Li; Liyuan Liu

doi:10.62762/JNSPM.2025.502885

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Journal of Numerical Simulations in Physics and Mathematics, Volume 1, Issue 2, 2025: 54-59

Open Access | Research Article | 18 September 2025

Exponential Inequality for the Dependent V-statistics of Bivariate Affine Functions

Richeng Zhou 1

Weifu Li 1

Liyuan Liu 1 *

1 College of Informatics, Huazhong Agricultural University, Wuhan 430070, China

* Corresponding Author: Liyuan Liu, [email protected]

DOI: 10.62762/JNSPM.2025.502885

Received: 04 September 2025, Accepted: 15 September 2025, Published: 18 September 2025

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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.

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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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