构建多模型不确定性联合分布理论框架，支持系统级决策
System-Level Uncertainty Quantification with Multiple Machine Learning Models: A Theoretical Framework
- 将模型与输入不确定性解耦为独立随机变量
- 给出多模型预测的联合概率分布计算方法
- 适用于需要可靠置信度的工程设计与决策场景
机器学习模型在预测时存在未知误差，可通过模型不确定性量化。当多个模型使用相同训练数据时，其不确定性可能存在统计依赖。实际中，模型输入本身也具有随机性，即输入不确定性。决策与设计必须考虑这两类不确定性的影响。本研究建立了一个理论框架，可在已知模型不确定性联合分布和输入联合分布的前提下，推导出多个模型预测的联合分布。核心策略是将两类不确定性解耦并转化为独立随机变量，为后续具体应用的数值算法开发奠定基础。
原文摘要 · Abstract (English)
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically dependent. In reality, model inputs are also random with input uncertainty. The effects of these types of uncertainty must be considered in decision-making and design. This study develops a theoretical framework that generates the joint distribution of multiple ML predictions given the joint distribution of model uncertainties and the joint distribution of model inputs. The strategy is to decouple the coupling between the two types of uncertainty and transform them as independent random variables. The framework lays a foundation for numerical algorithm development for various specific applications.
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