Lars Lindemann | Search arXiv

arXiv2026

Conformal Prediction Regions for Continuous-Time Trajectories under Random Sampling

Uncertainty quantification for continuous-time trajectories is a prerequisite in many safety-critical engineering domains. However, a major challenge in data-driven uncertainty quantification is that calibration trajectories are sampled only at discrete, often sparse, and random intervals. Standard conformal prediction methods typically fail to provide guarantees in between sampling times. In this work, we introduce a new technique to obtain valid conformal prediction regions for continuous-time trajectories that are sampled at discrete and possibly random times. To accomplish this goal, we make three contributions: (1) we provide an algorithm that leverages regularity properties of the underlying trajectories to obtain valid prediction regions in between samples, (2) we provide methods that estimate valid bounds on the aforementioned regularity properties from an additional high-frequency calibration dataset, and (3) we introduce and compare several algorithms to deal with random sampling times. Finally, we present experiments where we validate that our methods achieve valid coverage across the entire continuous trajectory.

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arXiv2026

A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification

Uncertainty quantification from finite data is central to machine learning, optimization, and automation systems, where decisions must remain reliable under limited samples and test-time distribution shift. Conformal prediction (CP) and distributionally robust optimization (DRO) offer two complementary approaches: CP constructs data-dependent prediction sets with distribution-free finite-sample validity under exchangeability, while DRO optimizes worst-case performance over an ambiguity set around an empirical distribution. We develop a unified probabilistic perspective on CP and DRO by viewing both as ways to turn finite calibration data into a data-dependent quantile estimator that a test score falls below with high probability. From this perspective, CP and DRO correct the empirical quantile along two coordinates of the same family of estimators: CP inflates the quantile level, whereas DRO shifts the quantile value through an ambiguity radius. Both methods provide the same calibration-conditional guarantee for the true distribution, requiring the target coverage to hold with high probability over the calibration sample. Their constructions differ, however: CP uses a closed-form, distribution-free level correction, while DRO uses a value-space correction whose certified radius depends on properties of the unknown distribution and additionally guarantees coverage uniformly over the ambiguity set. This distinction emerges in the tails of the score distribution. Because CP relies on sparse upper-tail order statistics of the calibration samples, its level inflation barely moves the estimator when those samples are dense near the target quantile but overshoots when they are sparse, whereas a well-chosen DRO radius corrects in value space and may avoid this overshoot.

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