Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks

• URL: http://arxiv.org/abs/2508.11025v1
• Date: Thu, 14 Aug 2025 19:03:28 GMT
• Title: Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks
• Authors: Laura Lützow, Michael Eichelbeck, Mykel J. Kochenderfer, Matthias Althoff,
• Abstract summary: Conformal prediction is used to augment a base predictor with prediction sets with statistically valid coverage guarantees.<n>We introduce zono-conformal prediction, a novel approach inspired by interval predictor models and reachset-conformant identification.<n>We show that zono-conformal predictors are less conservative than interval predictor models and standard conformal prediction methods.
• Score: 41.14877380522394
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Conformal prediction is a popular uncertainty quantification method that augments a base predictor with prediction sets with statistically valid coverage guarantees. However, current methods are often computationally expensive and data-intensive, as they require constructing an uncertainty model before calibration. Moreover, existing approaches typically represent the prediction sets with intervals, which limits their ability to capture dependencies in multi-dimensional outputs. We address these limitations by introducing zono-conformal prediction, a novel approach inspired by interval predictor models and reachset-conformant identification that constructs prediction zonotopes with assured coverage. By placing zonotopic uncertainty sets directly into the model of the base predictor, zono-conformal predictors can be identified via a single, data-efficient linear program. While we can apply zono-conformal prediction to arbitrary nonlinear base predictors, we focus on feed-forward neural networks in this work. Aside from regression tasks, we also construct optimal zono-conformal predictors in classification settings where the output of an uncertain predictor is a set of possible classes. We provide probabilistic coverage guarantees and present methods for detecting outliers in the identification data. In extensive numerical experiments, we show that zono-conformal predictors are less conservative than interval predictor models and standard conformal prediction methods, while achieving a similar coverage over the test data.

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