conformalized distance fields

In spatial statistics, reliable uncertainty quantification at unobserved locations under complex heterogeneity remains challenging: classical kriging relies on strong Gaussianity and stationarity assumptions, while existing machine learning approaches—including conformal prediction—often neglect spatial dependence, failing to guarantee conditional coverage in finite samples. We propose Spatial Conformal Quantile Regression (SCQR), the first method coupling localized quantile regression with conformal prediction. SCQR establishes theoretical guarantees under mild stationarity and spatial mixing (non-i.i.d.) conditions, jointly improving conditional coverage accuracy and prediction interval sharpness. Evaluated on synthetic and real-world spatial datasets, SCQR strictly achieves nominal coverage, yields narrower intervals, and exhibits stronger spatial coherence compared to both kriging and state-of-the-art spatial conformal methods.

Traditional conformal prediction (CP) provides only marginal coverage guarantees under small-sample calibration, exhibiting high variance in coverage distribution and frequent violations below the nominal level—thereby undermining reliability in uncertainty quantification. To address this, we propose a novel conformal prediction framework that, for the first time, delivers probabilistic coverage guarantees for individual predictors—e.g., $ mathbb{P}( ext{Coverage} geq 1-alpha) geq 1-delta $—overcoming the fundamental limitation of marginal guarantees. This guarantee holds rigorously even with limited calibration data and asymptotically recovers classical CP guarantees under large samples. Our method leverages nonparametric concentration inequalities, requires no assumptions on error distributions, and integrates seamlessly with mainstream CP libraries. Experiments demonstrate substantial improvements in coverage stability and safety under low-data regimes, providing verifiable statistical guarantees for uncertainty quantification in resource-constrained settings.

Traditional conformal prediction relies on p-values, distributional assumptions, and rank-based testing frameworks, limiting its applicability under weak supervision or unknown data distributions. To address this, we propose *conformal e-prediction*, a novel paradigm grounded in e-values—nonnegative random variables with expectation at most one under the null. This framework requires only exchangeability, enabling distribution-free uncertainty quantification valid at any time point. Our key contributions are: (1) the first integration of e-values into conformal prediction, supporting both batch online inference and data-dependent fixed-size prediction sets; (2) robustness under fuzzy ground-truth settings; and (3) anytime-valid inference with a data-driven coverage control algorithm that guarantees finite-sample validity of marginal coverage. By eliminating reliance on p-values and distributional assumptions, our approach significantly broadens the scope of conformal prediction to settings with limited supervision or unknown underlying distributions, striking a new balance between theoretical rigor and practical flexibility.

This work addresses the challenge of calibrated probabilistic forecasting for spatial point processes, such as tropical cyclone genesis and earthquake occurrences. The authors propose a novel conformal prediction framework that models spatial point clouds as empirical measures and employs (sliced) Wasserstein distance for scoring. A key innovation is the introduction of manifold constraints, which enforce predicted sets to adhere closely to the support manifold of the training data—a feature not previously explored in this context. The method provides theoretical lower bounds on coverage probability and incorporates a data-adaptive criterion to facilitate practical manifold selection. Experiments on synthetic, tropical cyclone, and earthquake datasets demonstrate that the approach achieves near-nominal coverage while significantly outperforming highest density region (HDR) methods and state-of-the-art generative baselines in terms of energy distance and manifold-aware metrics.

Traditional conformal prediction (CP) struggles with the structural complexity and dynamic nature of multimodal, streaming, and large-scale data. To address this, we reconceptualize CP from a data-centric perspective, proposing a novel methodological framework tailored to modern data science. Our approach designs calibration and ensemble construction strategies adaptable to structured, unstructured, and dynamically evolving data, integrating permutation tests, quantile regression, online learning, and adaptive reweighting—enabling distribution-free uncertainty quantification even for black-box models. It uniformly supports diverse modalities—including images, text, and time series—and introduces a new evaluation criterion that jointly optimizes validity and computational efficiency in large-model and big-data settings. Empirically, our framework significantly enhances CP’s applicability, scalability, and practical utility in real-world complex scenarios.

Full conformal prediction offers rigorous coverage guarantees but suffers from prohibitive computational costs, while existing approximate methods lack distribution-free theoretical assurances. This work proposes a novel approximation framework based on a “tournament” mechanism that, for the first time, achieves strict marginal coverage guarantees without retraining the model for every candidate response value. Under general conditions, the method attains $1 - 2\alpha$ coverage, and under a model stability assumption, it approaches the optimal $1 - \alpha$ coverage. The approach is compatible with existing approximation strategies, substantially reduces computational overhead, and demonstrates superior performance over current approximations both in theoretical guarantees and empirical predictive accuracy.

This work addresses the challenge of achieving safe and real-time motion planning in dynamic environments by effectively handling uncertainty in obstacle predictions. Existing approaches are limited in spatial consistency and computational scalability. To overcome these limitations, the paper introduces a Functional Conformal Prediction (FCP) framework—the first to apply conformal prediction to full distance fields rather than scalar errors. By modeling residual fields with low-rank and time-invariant structures, FCP generates distribution-free, decomposable, field-level safety lower bounds in coefficient space. The method integrates functional principal component analysis, Gaussian mixture-induced conformal prediction, and a lightweight online adaptive update (AFCP) into a sampling-based MPC formulation (FCP-MPC). Experiments on the ETH–UCY pedestrian datasets and a 3D quadrotor task with 280 dynamic obstacles demonstrate significant improvements in safety, trajectory feasibility, and computational efficiency, with per-step overhead substantially lower than existing online uncertainty-aware planners.

This work proposes an uncertainty-aware, interpretable framework for conformal prediction that addresses the limitations of traditional approaches relying on global calibration thresholds, which fail to distinguish instance-level sources of uncertainty or explain variations in prediction interval width. By introducing a localized calibration mechanism—applied progressively during the calibration process—the method enables instance-level diagnosis of reducible uncertainty in regression tasks. Integrating uncertainty decomposition with interpretability analysis, the framework uncovers task-specific patterns of epistemic uncertainty otherwise obscured by interval width. Experiments across multiple benchmark and real-world datasets demonstrate strong alignment between reducible uncertainty and proxy metrics of epistemic uncertainty, while quantifying how their relative contributions vary across tasks.

This work addresses the high computational cost of traditional conformal prediction, which requires refitting the model via leave-one-out (LOO) for every sample. We introduce, for the first time, approximate leave-one-out (ALO) from high-dimensional statistics into conformal prediction, constructing an efficient estimator of LOO residuals tailored to a new test point \(x_{n+1}\). This approach avoids repeated model retraining while substantially reducing computational overhead. Theoretical analysis demonstrates that the proposed method asymptotically preserves the coverage and predictive efficiency of exact LOO. Extensive experiments across diverse simulation settings confirm that it achieves comparable statistical performance with dramatically reduced runtime. Our study establishes a scalable, theoretically grounded, and practically viable paradigm for conformal prediction.

This study addresses the optimal split between training and calibration sets in split conformal prediction, aiming to simultaneously guarantee valid coverage probability and minimize prediction interval length under finite-sample settings. For the first time, we derive analytically the optimal split proportion that minimizes interval length in a general regression framework, and elucidate how factors such as model complexity influence this proportion. Combining theoretical analysis with a data-driven strategy, our approach is applicable across diverse models, including linear regression, nonparametric regression, and neural networks. Experimental results on both synthetic and real-world datasets demonstrate that the proposed splitting strategy substantially shortens prediction intervals while rigorously maintaining the prescribed coverage guarantees.