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.