Abstract
High-fidelity simulations are essential to scientific and engineering design, but can be expensive to run repeatedly. Learned surrogates offer a faster alternative, yet their higher errors may alter downstream decisions. This accuracy-speed tradeoff creates a need to determine whether a surrogate can be used or the full simulator remains necessary. We study decisions determined by whether a scalar quantity of interest lies above or below a fixed threshold. For each input, we use the surrogate when its conformal interval lies entirely on one side of the threshold and route the input to simulation when the interval intersects it. Standard conformal prediction constructs intervals without reference to the downstream decision threshold: even a narrow interval near the threshold can cross it and trigger simulation, whereas a wider interval farther away can remain entirely on one side and require no simulation. We introduce Threshold-Aware Conformal Routing (TACR), which learns an input-dependent scale using a threshold-aware objective that concentrates interval tightness near the decision boundary. Exact split-conformal calibration on held-out data preserves distribution-free marginal coverage, which also upper-bounds the probability of an incorrect threshold decision that is not routed. Across various scientific and engineering datasets, TACR reduces simulator deferrals by 14-75% relative to standard conformal prediction at the same coverage target. Against a variant without threshold-local weighting but with similar predictor accuracy, TACR further reduces deferrals by 10-24% on four datasets. These results show that optimizing interval allocation for routing can reduce simulator calls without weakening the standard conformal guarantee.
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Jun 9, 2026cs.LG
Conformal Prediction (CP) provides robust uncertainty guarantees for predictive models, but is typically applied post hoc, which misaligns model training with the conformal goal of producing efficient (i.e., narrow) intervals. We propose SPACR (Single-Pass Adaptive Conformal Regressor), a novel method for directly training uncertainty-aware regressors within a differentiable loss. SPACR jointly optimizes accuracy, efficiency, and validity without batch-splitting or a predefined confidence level during training. As a result, a single SPACR model yields valid prediction intervals at multiple confidence levels during inference, avoiding the costly retraining required by methods like Directly Optimized Inductive Conformal Regression (DOICR). Experiments on diverse tabular and image datasets show that SPACR consistently gives tighter intervals and better coverage-efficiency trade-offs compared to standard CP and DOICR, while significantly reducing computational costs relative to retraining-dependent baselines.
Soundouss Messoudi, Sylvain Rousseau, Sébastien Destercke
Heudiasyc - UMR CNRS 7253, Université de Technologie de Compiègne
Jun 30, 2026stat.ML
While conformal prediction provides a general framework for uncertainty quantification in predictive inference, its application is often limited by computational cost. Recent methods, including Jackknife+ and Jackknife-minmax, achieve faster computation by trading a slight loss of efficiency relative to full conformal prediction, but still requires computing leave-one-out refits for all observations. In this paper, we further accelerate conformal prediction by incorporating approximate leave-one-out (ALO) estimators, and establish asymptotic coverage and efficiency. While our proof draws on methods developed for analyzing the consistency of ALO cross-validation risk estimators in high-dimensional statistics, it requires adaptations to handle conformal prediction, where leave-
i-out residuals are needed for predictions at
xn+1 rather than just at the training covariate
xi. Simulation results validate our theoretical findings, showing that the ALO-based methods achieve coverage and efficiency comparable to the exact methods, while significantly reducing the runtime.
Jiachen Cong, Jingbo Liu
Department of Statistics, University of Illinois Urbana-Champaign, Champaign, IL, 61820, USA
May 9, 2026cs.LG
Recent advances in uncertainty quantification for time series forecasting show that conformal prediction can provide reliable prediction intervals, yet standard conformal methods are often inefficient under temporal dependence, drift, and heterogeneous error behavior. Existing methods typically either update miscoverage rates over time or learn unconstrained calibration weights, without explicitly separating two central sources of nonstationarity: smoothly drifting error distributions and co-existing distinct error regimes. We introduce RareCP, a regime-aware retrieval method for adaptive conformal time series prediction. RareCP learns local calibration representations through a mixture of cosine-attention experts that each capture distinct error regimes, while a compact hypernetwork adapts the kernel parameters to track temporal drift. Given a new forecasting context, RareCP retrieves the top-k most relevant calibration examples, assigns similarity weights, and forms a weighted conformal quantile over their signed residuals, yielding asymmetric prediction intervals. The adaptive kernel is trained using a smooth interval score objective, with a parameter-space anchor to a lightweight teacher kernel to preserve stable local representations. On the GIFT-Eval benchmark, RareCP improves interval efficiency over recent conformal baselines and foundation model uncertainty estimates while maintaining empirical coverage. Ablations confirm that regime-specific experts, drift-adaptive kernels, sparse retrieval, and teacher anchoring each contribute to the final performance.
Manuel Heurich, Maximilian Granz, Tim Landgraf
Institute for Computer Science Freie Universität Berlin Arnimallee 7 14195 Berlin