The paper presents a conformal prediction framework for regression problems where the responses lie on the Grassmann manifold. It builds prediction regions as metric balls on the manifold, using basis‑invariant geometric distances as non‑conformity measures and scaling them with a learned prediction‑difficulty estimator to achieve locally adaptive, input‑dependent regions. The method preserves finite‑sample marginal coverage under exchangeability and is evaluated on synthetic data and an airfoil inverse shape‑design task, showing that geometry‑aware scores and local adaptation improve coverage uniformity and can reduce region size in heteroscedastic settings.
arXiv:2602. 16015v2 Announce Type: replace Abstract: Conformal prediction gives finite-sample coverage guarantees for regression, but most standard constructions are designed for Euclidean output spaces.
The paper introduces a tail‑aware geometry learning framework for multivariate conformal prediction using ellipsoids. It decouples tail sensitivity from coverage guarantees by learning a metric matrix through volume minimization under a CVaR constraint, followed by standard conformal calibration. The approach is convex, prioritizes high‑residual samples, and theoretically balances ellipsoidal volume against tail severity, with experiments confirming its effectiveness.
arXiv:2605.08506v3 Announce Type: replace Abstract: Robust optimization (RO) provides a principled framework for decision-making under uncertainty, but its performance critically depends on the choic...
arXiv:2606. 31915v1 Announce Type: cross Abstract: While conformal prediction provides a general framework for uncertainty quantification in predictive inference, its application is often limited by computational cost.
arXiv:2501.18060v2 Announce Type: replace-cross Abstract: Conformal inference provides a rigorous statistical framework for uncertainty quantification in machine learning, enabling well-calibrated pr...
arXiv:2610.00535v1 Announce Type: new Abstract: Uncertainty quantification is critical in scientific machine learning, where black-box, image-based models are increasingly deployed in high-stakes set...
arXiv:2603.23923v2 Announce Type: replace-cross Abstract: Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution an...
arXiv:2601. 13102v3 Announce Type: replace-cross Abstract: Full conformal prediction is a framework that implicitly formulates distribution-free confidence prediction regions for a wide range of estimators.
arXiv:2606. 31600v1 Announce Type: cross Abstract: Conformal prediction and its variants, including the split conformal prediction, provide a distribution-free framework for uncertainty quantification by constructing prediction intervals or sets with finite-sample coverage guarantees.
arXiv:2602. 01733v3 Announce Type: replace-cross Abstract: Conformal Prediction (CP) provides a statistical framework for uncertainty quantification that constructs prediction sets with coverage guarantees.
The paper introduces the conditional expected local radius (CELR), a new tool for measuring local conditional probability concentration in general metric spaces. Using CELR, the authors develop a conformal prediction method that works for non‑Euclidean responses, accommodates heterogeneity and multimodality without requiring densities or vector‑space structure, and avoids costly transport comparisons. The method is implemented via a metric distributional random forest that handles multivariate covariates and nonlinear interactions, yielding uniform consistency, asymptotic conditional validity, and finite‑sample marginal coverage under exchangeability, while also providing substantial computational savings compared to existing approaches.
arXiv:2606. 15760v1 Announce Type: new Abstract: A significant gap exists between theory and practice in deep learning.