TL;DR
This paper introduces Local Sliced Conformal Inference (LSCI), a new distribution-free method for producing locally adaptive, calibrated uncertainty sets for operator models used in spatiotemporal forecasting, with proven validity and improved performance.
Contribution
The paper presents LSCI, a novel framework for uncertainty quantification in operator models, with theoretical guarantees and superior empirical adaptivity and robustness.
Findings
LSCI provides tighter, more adaptive prediction sets than baselines.
LSCI maintains finite-sample validity and coverage guarantees.
Empirical results show robustness against bias and out-of-distribution noise.
Abstract
Operator models are regression algorithms between Banach spaces of functions. They have become an increasingly critical tool for spatiotemporal forecasting and physics emulation, especially in high-stakes scenarios where robust, calibrated uncertainty quantification is required. We introduce Local Sliced Conformal Inference (LSCI), a distribution-free framework for generating function-valued, locally adaptive prediction sets for operator models. We prove finite-sample validity and derive a data-dependent upper bound on the coverage gap under local exchangeability. On synthetic Gaussian-process tasks and real applications (air quality monitoring, energy demand forecasting, and weather prediction), LSCI yields tighter sets with stronger adaptivity compared to conformal baselines. We also empirically demonstrate robustness against biased predictions and certain out-of-distribution noise…
Peer Reviews
Decision·Submitted to ICLR 2026
1. The paper is technically sound 2. The paper has strong empirical evidence and is convincing. The experiments show it produces prediction bands that are appropriately tight in low-variance regions and wider in high-variance regions, leading to more informative and useful uncertainty estimates. 3. The theory relies on local exchangeability, a far more realistic assumption for complex, non-stationary data than the standard global exchangeability required by standard CP methods. 4. The authors pr
1. The method's adaptivity hinges on the choice of the localization kernel H, the bandwidth lambda, and potentially a feature map phi. While the paper ablates these (in fig 1) and suggests tuning lambda, it offers little guidance on how to choose H or other hyperparameters and analyzes how it affects the resulting efficiency. A discussion on how to choose these parameters would be beneficial. 2. While weaker than global exchangeability, the assumption that residual distributions vary smoothly co
The authors validate their method with an intuitive upper bound for the coverage gap, which makes it clear how coverage suffers when local exchangeability is weakened. The experiments are quite robust and further strengthen their proposed method.
Main Weaknesses * The proposed method isn’t well-motivated. The paper didn’t cite any examples where global exchangeability might break or local exchangeability might hold with functional data. * It’s not easy to see why depth-based scores are important to obtain local marginal coverage or tight prediction sets. In experiments, it’s clear that LSCI outperforms all the conformal baselines in the Interval Score metric, but there is no intuition behind why depth-based score can reduce Interval sco
The authors employ the tool of $\Phi$-depths to establish conformity measures suitable for functional data. Additionally, the authors utilize local information to construct the score function, thereby endowing the proposed method with enhanced robustness.
1. For methodology, in the literature on localized prediction sets (e.g., Guan, 2023[1]; Hore & Barber, 2023[2]; Barber, 2023[3]), the threshold $q_{\alpha}(f_{n+1})$ is typically defined as the $1-\alpha$ quantile of a weighted distribution $\sum_{i=1}^{n+1}w_i\delta_i$, where the weight $w_i$ assigned to each data point reflects its contribution to the construction of the prediction set. However, in line 201, the authors adopt a different quantile definition. Constructing prediction sets in th
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