Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks
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| Format: | Preprint |
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2025
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| _version_ | 1866915832585519104 |
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| author | Lützow, Laura Eichelbeck, Michael Kochenderfer, Mykel J. Althoff, Matthias |
| author_facet | Lützow, Laura Eichelbeck, Michael Kochenderfer, Mykel J. Althoff, Matthias |
| contents | Conformal prediction is a popular uncertainty quantification method that augments a base predictor to return sets of predictions 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks Lützow, Laura Eichelbeck, Michael Kochenderfer, Mykel J. Althoff, Matthias Machine Learning Artificial Intelligence Systems and Control Conformal prediction is a popular uncertainty quantification method that augments a base predictor to return sets of predictions 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. |
| title | Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks |
| topic | Machine Learning Artificial Intelligence Systems and Control |
| url | https://arxiv.org/abs/2508.11025 |