{"ID":2856558,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11871","arxiv_id":"2510.11871","title":"Active Subspaces in Infinite Dimension","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 and improve modeling and optimization on complex test problems.","short_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...","url_abs":"https://arxiv.org/abs/2510.11871","url_pdf":"https://arxiv.org/pdf/2510.11871v1","authors":"[\"Poorbita Kundu\",\"Nathan Wycoff\"]","published":"2025-10-13T19:30:55Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}