Active Subspaces in Infinite Dimension

Poorbita Kundu, Nathan Wycoff
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:2089-2097, 2026.

Abstract

Active subspace analysis uses the leading eigenspace of the gradient’s second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a Euclidean space. We show that many of the desirable properties of Active Subspace analysis extend directly to the infinite dimensional setting. We also propose a Monte Carlo procedure and discuss its convergence properties. Finally, we deploy this methodology to create visualizations as well as improve modeling and optimization on complex test problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-kundu26a, title = { Active Subspaces in Infinite Dimension }, author = {Kundu, Poorbita and Wycoff, Nathan}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {2089--2097}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/kundu26a/kundu26a.pdf}, url = {https://proceedings.mlr.press/v300/kundu26a.html}, abstract = { Active subspace analysis uses the leading eigenspace of the gradient’s second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a Euclidean space. We show that many of the desirable properties of Active Subspace analysis extend directly to the infinite dimensional setting. We also propose a Monte Carlo procedure and discuss its convergence properties. Finally, we deploy this methodology to create visualizations as well as improve modeling and optimization on complex test problems. } }
Endnote
%0 Conference Paper %T Active Subspaces in Infinite Dimension %A Poorbita Kundu %A Nathan Wycoff %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-kundu26a %I PMLR %P 2089--2097 %U https://proceedings.mlr.press/v300/kundu26a.html %V 300 %X Active subspace analysis uses the leading eigenspace of the gradient’s second moment to conduct supervised dimension reduction. In this article, we extend this methodology to real-valued functionals on Hilbert space. We define an operator which coincides with the active subspace matrix when applied to a Euclidean space. We show that many of the desirable properties of Active Subspace analysis extend directly to the infinite dimensional setting. We also propose a Monte Carlo procedure and discuss its convergence properties. Finally, we deploy this methodology to create visualizations as well as improve modeling and optimization on complex test problems.
APA
Kundu, P. & Wycoff, N.. (2026). Active Subspaces in Infinite Dimension . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:2089-2097 Available from https://proceedings.mlr.press/v300/kundu26a.html.

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