Consistency of Dictionary-Based Manifold Learning
Abstract
We analyze a paradigm for interpretable Manifold Learning for scientific data analysis, whereby one parametrizes a manifold with d smooth functions from a scientist-provided dictionary of meaningful, domain-related functions. When such a parametrization exists, we provide an algorithm for finding it based on sparse regression in the manifold tangent bundle, bypassing more standard, agnostic manifold learning algorithms. We prove conditions for the existence of such parameterizations in function space and the first end to end recovery results from finite samples. The method is demonstrated on both synthetic problems and with data from a real scientific domain.
Cite
Text
Koelle et al. "Consistency of Dictionary-Based Manifold Learning." Artificial Intelligence and Statistics, 2024.Markdown
[Koelle et al. "Consistency of Dictionary-Based Manifold Learning." Artificial Intelligence and Statistics, 2024.](https://mlanthology.org/aistats/2024/koelle2024aistats-consistency/)BibTeX
@inproceedings{koelle2024aistats-consistency,
title = {{Consistency of Dictionary-Based Manifold Learning}},
author = {Koelle, Samson J. and Zhang, Hanyu and Murad, Octavian-Vlad and Meila, Marina},
booktitle = {Artificial Intelligence and Statistics},
year = {2024},
pages = {4348-4356},
volume = {238},
url = {https://mlanthology.org/aistats/2024/koelle2024aistats-consistency/}
}