用一种新方法生成带置信保证的预测集合,更高效且能捕捉多维依赖关系。
Zono-Conformal Prediction: Zonotope-Based Uncertainty Quantification for Regression and Classification Tasks
- 通过线性规划直接构建带保证覆盖的预测多面体,无需复杂校准
- 在回归与分类任务中均实现比传统方法更紧致的预测集,覆盖率达标
- 适合需要高可靠性预测的场景,如自动驾驶、医疗诊断
置信预测是一种流行的不确定性量化方法,可为基线预测器提供具有统计覆盖保证的预测集合。然而,现有方法通常计算成本高且依赖大量数据,因需先构建不确定性模型再进行校准。此外,多数方法使用区间表示预测集,难以捕捉多维输出间的依赖关系。本文提出基于区域的置信预测(zono-conformal prediction),受区间预测模型和可达集一致识别启发,直接在基线预测器中引入区域不确定性集,通过单次高效线性规划即可识别预测多面体,确保覆盖概率。该方法适用于任意非线性基线预测器,本文聚焦前馈神经网络。不仅用于回归任务,也构建了分类任务下的最优预测多面体,输出可能类别集合。提供概率覆盖保证,并给出识别数据中异常值的检测方法。大量数值实验表明,相比区间预测模型和标准置信预测,该方法更不保守,同时保持相当的测试覆盖率。
原文摘要 · Abstract (English)
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.
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