Consistent Interpolating Ensembles via the Manifold-Hilbert Kernel
Authors: Yutong Wang, Clay Scott
NeurIPS 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble methods. We devise an ensemble classification method that simultaneously interpolates the training data, and is consistent for a broad class of data distributions. To this end, we define the manifold-Hilbert kernel for data distributed on a Riemannian manifold. We prove that kernel smoothing regression and classification using the manifold-Hilbert kernel are weakly consistent in the setting of Devroye et al. [22]. For the sphere, we show that the manifold-Hilbert kernel can be realized as a weighted random partition kernel, which arises as an infinite ensemble of partition-based classifiers. |
| Researcher Affiliation | Academia | Yutong Wang University of Michigan yutongw@umich.edu Clayton D. Scott University of Michigan clayscot@umich.edu |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | No | The paper does not provide any explicit statement or link to open-source code for the described methodology. In the 'If you ran experiments...' section, all items related to code and data are marked as N/A. |
| Open Datasets | No | The paper is theoretical and does not mention the use of any specific public or open dataset for training experiments. The 'If you ran experiments...' section states N/A for experimental details. |
| Dataset Splits | No | The paper is theoretical and does not provide specific dataset split information (e.g., percentages, sample counts) for training, validation, or test sets. The 'If you ran experiments...' section states N/A for experimental details. |
| Hardware Specification | No | The paper is theoretical and does not describe any specific hardware used to run experiments. The 'If you ran experiments...' section states N/A for experimental details like compute resources. |
| Software Dependencies | No | The paper is theoretical and does not provide specific software dependencies (e.g., library names with version numbers) needed to replicate experiments. The 'If you ran experiments...' section states N/A for experimental details. |
| Experiment Setup | No | The paper is theoretical and does not provide specific details about an experimental setup, such as hyperparameters or system-level training settings. The 'If you ran experiments...' section states N/A for experimental details like training details. |