Metraipolis › archive › dc_c8a2b74bb482

Multi-Task Learning of Conditional Mean Operators: applications to dynamical systems and uncertainty quantification — arXiv:2609.35429

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.35429
License (as archived): CC0-1.0
Archived: 2026-10-07T22:41:12.406Z
SHA-256 of the archived text: d9e1131e8462c314d631d6703d7d1006461d85bd0d0154cef24e614190384b6a
Stable URL of this page: https://metraipolis.com/documento/dc_c8a2b74bb482

How to cite

Multi-Task Learning of Conditional Mean Operators: applications to dynamical systems and uncertainty quantification — arXiv:2609.35429 — arXiv (en), https://arxiv.org/abs/2609.35429 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c8a2b74bb482 (Metraipolis archive dc_c8a2b74bb482, sha256 d9e1131e8462c314d631d6703d7d1006461d85bd0d0154cef24e614190384b6a)

BibTeX

@misc{dcc8a2b74bb482,
  title = {Multi-Task Learning of Conditional Mean Operators: applications to dynamical systems and uncertainty quantification — arXiv:2609.35429},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.35429},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c8a2b74bb482; sha256 d9e1131e8462c314d631d6703d7d1006461d85bd0d0154cef24e614190384b6a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.35429. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Estimating conditional statistics and learning representations of a population of conditional distributions are central problems in many data-driven applications, including uncertainty quantification and dynamical systems analysis. Conditional mean operators (CMOs), a class of linear operators between function spaces, resolve these objectives by providing access to a broad class of conditional statistics. However, existing methods typically estimate each CMO independently or constrain it to prespecified function spaces, thereby preventing the exploitation of shared structure across related distributions. In this work, we posit that related CMOs share finite-dimensional input and output function spaces, and are specialized for each task with a linear operator mapping these spaces. Based on this hypothesis, we introduce MTL-CMO, a multi-task framework that jointly learns shared function spaces and task-specific operators across multiple datasets. We further introduce T-CMO, a transfer learning method that reuses the shared spaces to estimate, in closed form, the operator of a new conditional distribution. We establish statistical guarantees quantifying the benefits of jointly learning the shared function spaces. Our experiments demonstrate that learning shared function spaces improves uncertainty quantification across a broad range of conditional distributions and, when applied to Langevin and plasma dynamics, yields compact representations of complex dynamics that retain physically meaningful information and enable parameter identification.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-29 in cs.LG).
Categorie arXiv: Machine Learning (stat.ML) ; Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2609.35429 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T22:14:28.925Z dalla pagina https://arxiv.org/catchup/cs.LG/2026-09-29?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).