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.

翻译：Conformal预测是一种流行的不确定性量化方法，它通过增强基础预测器来返回具有统计有效覆盖保证的预测集合。然而，现有方法通常计算成本高昂且数据密集，因为它们在标定前需要构建不确定性模型。此外，现有方法通常用区间表示预测集合，这限制了其捕捉多维输出间依赖关系的能力。为克服这些限制，我们提出zono-conformal预测——一种受区间预测器模型和可达集一致性辨识启发的新方法，可构建具有保证覆盖度的预测zonotope。通过将zonotopic不确定性集合直接嵌入基础预测器模型，zono-conformal预测器可通过单一且数据高效的线性规划进行辨识。虽然zono-conformal预测可应用于任意非线性基础预测器，但本文主要聚焦前馈神经网络。除回归任务外，我们还在分类场景中构建了最优zono-conformal预测器，其中不确定性预测器的输出是可能的类别集合。我们提供了概率覆盖保证，并提出了辨识数据中异常值的检测方法。在大量数值实验中，我们证明zono-conformal预测器比区间预测器模型和标准conformal预测方法更少保守，同时在测试数据上实现了相似的覆盖度。