Provably Strict Generalisation Benefit for Invariance in Kernel Methods
Authors: Bryn Elesedy
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this work we build on the function space perspective of Elesedy and Zaidi [8] to derive a strictly non-zero generalisation benefit of incorporating invariance in kernel ridge regression when the target is invariant to the action of a compact group. We study invariance enforced by feature averaging and find that generalisation is governed by a notion of effective dimension that arises from the interplay between the kernel and the group. In building towards this result, we find that the action of the group induces an orthogonal decomposition of both the reproducing kernel Hilbert space and its kernel, which may be of interest in its own right. |
| Researcher Affiliation | Academia | Bryn Elesedy University of Oxford bryn@robots.ox.ac.uk |
| Pseudocode | No | The paper presents theoretical derivations and theorems but does not include any explicitly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | In the 'Questions for Paper Analysis' section, the authors state '[N/A]' for 'Did you include the code, data, and instructions needed to reproduce the main experimental results'. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments involving training data. In the 'Questions for Paper Analysis' section, the authors state '[N/A]' for 'Did you include the code, data, and instructions needed to reproduce the main experimental results'. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments, therefore no validation split information is provided. In the 'Questions for Paper Analysis' section, the authors state '[N/A]' for 'Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?'. |
| Hardware Specification | No | The paper is theoretical and does not conduct experiments, therefore no hardware specifications are provided. In the 'Questions for Paper Analysis' section, the authors state '[N/A]' for 'Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)?'. |
| Software Dependencies | No | The paper is theoretical and does not describe experimental implementations, thus it does not list specific software dependencies with version numbers. |
| Experiment Setup | No | The paper is theoretical and does not conduct experiments, thus no experimental setup details like hyperparameters or training configurations are provided. In the 'Questions for Paper Analysis' section, the authors state '[N/A]' for 'Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)?'. |