用流模型高效生成高维不确定预测边界，支持采样与概率预报。
Flow-Based Conformal Predictive Distributions
- 基于可微非契合度得分构造确定性流，逼近预测集边界。
- 无需训练即可在任意维度采样，且分位数区域匹配实测预测集。
- 适用于物理建模、气候预测等需不确定性量化场景。
置信预测提供了一种分布无关的不确定性量化框架，通过具有精确有限样本覆盖率的预测集实现。在低维情况下这些集合易于解释，但在高维或结构化输出空间中难以表示和使用，限制了其与下游任务（如采样和概率预报）的集成。我们证明，任何足够光滑的可微非契合度得分都会在输出空间上诱导出一个确定性流，其轨迹收敛至对应预测集的边界。这带来了一种计算高效的、无需训练的方法，可在任意维度采样预测边界。通过混合不同置信水平，得到的置信预测分布的分位数区域恰好与经验预测集一致。我们给出了一个近似误差分解边界，将预测误差分解为得分引起的畸变、基度量质量以及梯度流引起的畸变三部分。我们在偏微分方程反问题、降水降尺度、气候模型去偏和飓风路径预测等任务上进行了评估。
原文摘要 · Abstract (English)
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured output spaces they are difficult to represent and use, which can limit their ability to integrate with downstream tasks such as sampling and probabilistic forecasting. We show that any sufficiently regular differentiable nonconformity score induces a deterministic flow on the output space whose trajectories converge to the boundary of the corresponding conformal prediction set. This leads to a computationally efficient, training-free method for sampling conformal boundaries in arbitrary dimensions. Mixing across confidence levels yields conformal predictive distributions whose quantile regions coincide with the empirical conformal prediction sets. We provide an approximation bound decomposing CPD predictive error into score-induced distortion, base-measure quality, and gradient flow-induced distortion. We evaluate the approach on PDE inverse problems, precipitation downscaling, climate model debiasing, and hurricane trajectory forecasting.
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