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Locally Adaptive Conformal Prediction for Polynomial Chaos Expansions — arXiv:2611.09579

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.09579
License (as archived): CC0-1.0
Archived: 2026-11-09T22:42:14.839Z
SHA-256 of the archived text: aa2c58c83807f17dbf8630d9dffda43c661375675be12183d0ecd39678f1f73a
Stable URL of this page: https://metraipolis.com/documento/dc_9980d10ec2ea

How to cite

Locally Adaptive Conformal Prediction for Polynomial Chaos Expansions — arXiv:2611.09579 — arXiv (en), https://arxiv.org/abs/2611.09579 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_9980d10ec2ea (Metraipolis archive dc_9980d10ec2ea, sha256 aa2c58c83807f17dbf8630d9dffda43c661375675be12183d0ecd39678f1f73a)

BibTeX

@misc{dc9980d10ec2ea,
  title = {Locally Adaptive Conformal Prediction for Polynomial Chaos Expansions — arXiv:2611.09579},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.09579},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_9980d10ec2ea; sha256 aa2c58c83807f17dbf8630d9dffda43c661375675be12183d0ecd39678f1f73a},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.09579. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

This work develops a locally adaptive jackknife+ conformal prediction framework for polynomial chaos expansions. Therein, the non-conformity scores are normalized with an auxiliary polynomial chaos expansion trained on the log-transformed leave-one-out residuals of the base model. We show that the coverage guarantee of jackknife+ conformal prediction carries over to the adaptive intervals if the leave-one-out auxiliary models are trained on nested leave-one-out residuals. For fixed-basis polynomial chaos expansions fitted by ordinary least squares, all required quantities are derived in closed form and the guarantee-preserving adaptive intervals are obtained from a single model fit, without any model retraining. For sparse polynomial chaos expansions, where multiple model fits are necessary, we propose a heuristic simplification that limits the computational overhead of adaptivity at the cost of the formal coverage guarantee. Numerical experiments on an academic benchmark with known heteroscedastic noise and on an engineering simulation dataset show that the suggested method attains the target coverage while providing intervals that adapt to local prediction uncertainty, therefore being considerably more statistically efficient. These advantages are particularly prominent in high-uncertainty regions of the input space, where the performance of non-adaptive methods degrades substantially.

Tema degli esploratori: statistica e scienza dei dati (elenco arXiv stat.ML, nuovi lavori del giorno).
Categorie arXiv: Computation (stat.CO) ; Computational Engineering, Finance, and Science (cs.CE); Methodology (stat.ME); Machine Learning (stat.ML).
Pagina del lavoro: https://arxiv.org/abs/2611.09579 — 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 2026-11-09T22:34:32.285Z dalla pagina https://arxiv.org/list/stat.ML/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).