Towards Unified Native Spaces in Kernel Methods
Authors: Xavier Emery, Emilio Porcu, Moreno Bevilacqua
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper unifies a wealth of well-known kernels into a single parametric class that encompasses them as special cases, attained either by exact parameterization or through parametric asymptotics. We furthermore find parametric restrictions under which we can characterize the Sobolev space that is norm equivalent to the RKHS associated with the new kernel. As a by-product, we infer the Sobolev spaces that are associated with existing classes of kernels. |
| Researcher Affiliation | Academia | Xavier Emery EMAIL Department of Mining Engineering, Universidad de Chile Santiago 8370448, Chile & Advanced Mining Technology Center, Universidad de Chile Santiago 8370448, Chile Emilio Porcu EMAIL Department of Mathematics, Khalifa University Abu Dhabi 127788, United Arab Emirates & ADIA Lab Abu Dhabi 127788, United Arab Emirates Moreno Bevilacqua EMAIL Facultad de Ingenieria y Ciencias, Universidad Adolfo Iba nez Vi na del Mar 2580335, Chile & Dipartimento di Scienze Ambientali, Informatica e Statistica, Ca Foscari University of Venice Venice 30123, Italy |
| Pseudocode | No | The paper describes mathematical properties and theoretical derivations of kernel functions, but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statements about the release of source code for the methodology described, nor does it include links to any code repositories. |
| Open Datasets | No | This paper is purely theoretical, focusing on the mathematical properties and parameterizations of kernel functions. It does not present any experiments or use any datasets. |
| Dataset Splits | No | This theoretical paper does not use any datasets for experiments, therefore, there is no information on dataset splits. |
| Hardware Specification | No | The paper presents theoretical research on kernel methods and does not describe any experiments that would involve specific hardware specifications. |
| Software Dependencies | No | The paper is theoretical and focuses on mathematical derivations and properties of kernel functions. It does not mention any specific software dependencies with version numbers for experimental implementation. |
| Experiment Setup | No | This paper is theoretical in nature, focusing on the mathematical properties of kernel functions. It does not include any experimental setup details or hyperparameters. |