arXiv：cs.LG· Jose Cribeiro-Ramallo, Florian Kalinke, Zolt\'an Szab\'o·· 4 小时前AI 评分24
无界核的特征性与通用性：核方法表达能力概念间的关系研究
Unbounded Characteristic and Universal Kernels
AI 导读
核方法中特征性、L_p-通用性和积分严格正定等概念刻画了核及其RKHS的表达能力，但有界核情形下这些概念的关系已被充分理解，无界核情形下却鲜有研究。该论文在温和假设下建立了无界核上述表达能力概念之间的关系，填补了这一空白。
正文
Abstract:Kernel methods are among the most powerful tools in machine learning and statistics, with a large number of successful applications. Their immense success stems from the flexible function class associated to each kernel---its reproducing kernel Hilbert space (RKHS)---which facilitates statistical analysis, as well as from their computational tractability and applicability to many domains. Multiple notions (such as characteristic, $L_p$-universal, and integrally strictly positive definite) capture the expressivity of kernels and their RKHSs and play a key role in understanding the statistical properties of kernel methods; these concepts and their relations are well-understood for bounded kernels. Even though unbounded kernels have received significant attention over the past decade (for instance, in the construction of kernel-based discrepancy and dependence measures such as the maximum mean discrepancy, the Hilbert-Schmidt independence criterion, and the kernel Stein discrepancy), surprisingly little is known about the relations of these notions in the unbounded case. In the present paper we tackle this severe bottleneck, establishing their relations under mild assumptions.
| Subjects: | Statistics Theory (math.ST); Machine Learning (cs.LG); Machine Learning (stat.ML) |
| MSC classes: | 46E22 (Primary) 62B10, 46N30 (Secondary) |
| ACM classes: | G.3; H.1.1; I.2.6 |
| Cite as: | arXiv:2610.09731 [math.ST] |
| (or arXiv:2610.09731v1 [math.ST] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09731 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jose Cribeiro-Ramallo [view email]
[v1]
Wed, 7 Oct 2026 09:25:31 UTC (38 KB)
来源：arXiv：cs.LG · arxiv.org