The Confidence Score: a New Measure on Kernels

Computer Science > Machine Learning arXiv:2611.05528 (cs) [Submitted on 3 Nov 2026] Title: The Confidence Score: a New Measure on Kernels Authors: Elizabeth Hofer, Martin v. Mohrenschildt.

计算机科学 > 机器学习 arXiv:2611.05528 (cs) [提交于 2026 年 11 月 3 日] 标题：《置信度评分：一种新的核函数度量方法》 作者：Elizabeth Hofer, Martin v. Mohrenschildt。

Abstract: Across a wide range of applications, kernel measures are used to tune hyperparameters, select among candidate kernels, and assess the suitability of kernels for specific learning tasks. For classification, kernel measures are used to predict which kernels may produce accurate kernel classifiers.

摘要：在广泛的应用中，核度量被用于调整超参数、在候选核之间进行选择，以及评估核函数对于特定学习任务的适用性。在分类任务中，核度量被用于预测哪些核函数能够产生准确的核分类器。

Many existing kernel measures, such as alignment to the ideal kernel, are designed to reward kernels which captures all samples from the same class as similar. While effective in many settings, this requirement is unnecessarily restrictive for classification, where classes may exhibit substantial internal structure.

许多现有的核度量方法（例如与理想核的对齐）旨在奖励那些将同一类中的所有样本视为相似的核函数。虽然在许多场景下有效，但对于分类任务而言，这一要求过于严苛，因为类别本身可能表现出显著的内部结构。

In this work, the “Confidence Score”, a new kernel measure, is proposed. Unlike alignment-to-the-ideal kernel measures, the Confidence Score measures the alignment between an encoding of the ground truth and that ground truth projected by the kernel, allowing kernels that preserve intra-class structure to achieve high scores.

在这项工作中，提出了一种新的核度量方法——“置信度评分”（Confidence Score）。与“与理想核对齐”的度量方法不同，置信度评分衡量的是真实标签的编码与核函数投影出的真实标签之间的对齐程度，从而允许那些能够保留类内结构的核函数获得高分。

Through experiments, it is demonstrated that the Confidence Score exhibits a higher correlation with classification accuracy across a variety of kernels on both real-world and synthetic datasets, compared to select other kernel measures.

通过实验证明，与选定的其他核度量方法相比，置信度评分在真实世界和合成数据集的各种核函数上，与分类准确率表现出更高的相关性。