Consistency of Dictionary-Based Manifold Learning

Samson J. Koelle, Hanyu Zhang, Octavian-Vlad Murad, Marina Meila
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:4348-4356, 2024.

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 this Paper

BibTeX
@InProceedings{pmlr-v238-koelle24a, title = {Consistency of Dictionary-Based Manifold Learning}, author = {Koelle, Samson J. and Zhang, Hanyu and Murad, Octavian-Vlad and Meila, Marina}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {4348--4356}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/koelle24a/koelle24a.pdf}, url = {https://proceedings.mlr.press/v238/koelle24a.html}, 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.} }
Endnote
%0 Conference Paper %T Consistency of Dictionary-Based Manifold Learning %A Samson J. Koelle %A Hanyu Zhang %A Octavian-Vlad Murad %A Marina Meila %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-koelle24a %I PMLR %P 4348--4356 %U https://proceedings.mlr.press/v238/koelle24a.html %V 238 %X 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.
APA
Koelle, S.J., Zhang, H., Murad, O. & Meila, M.. (2024). Consistency of Dictionary-Based Manifold Learning. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:4348-4356 Available from https://proceedings.mlr.press/v238/koelle24a.html.

Related Material