On the Consistency of Kernel Methods with Dependent Observations

Authors: Pierre-François Massiani, Sebastian Trimpe, Friedrich Solowjow

ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We propose the new notion of empirical weak convergence (EWC) as a general assumption explaining such phenomena for kernel methods. Our main results then establish consistency of SVMs, kernel mean embeddings, and general Hilbert-space valued empirical expectations with EWC data. Our analysis holds for both finite- and infinite-dimensional outputs, as we extend classical results of statistical learning to the latter case. Overall, our results open new classes of processes to statistical learning and can serve as a foundation for a theory of learning beyond i.i.d. and mixing.
Researcher Affiliation Academia 1Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Aachen, Germany.
Pseudocode No The paper focuses on theoretical derivations and proofs, and does not include any pseudocode or algorithm blocks.
Open Source Code No The paper does not mention releasing any open-source code for the described methodology.
Open Datasets No The paper is theoretical and does not conduct experiments with datasets.
Dataset Splits No The paper is theoretical and does not conduct experiments with datasets, so no training/validation/test splits are discussed.
Hardware Specification No The paper is theoretical and does not report on experimental setup, thus no hardware specifications are provided.
Software Dependencies No The paper is theoretical and does not report on experimental setup, thus no software dependencies are listed.
Experiment Setup No The paper is theoretical and does not describe an experimental setup with hyperparameters or training settings.