🤖 AI Summary
In multi-model prediction, system reliability is jointly affected by model uncertainty—arising from statistical dependencies among models trained on shared data—and input uncertainty—stemming from the inherent randomness of inputs. Existing methods fail to simultaneously and rigorously quantify these two distinct uncertainty sources. This paper proposes the first theoretical framework that explicitly decouples inter-model dependencies from input stochasticity, treating them as independent variables and constructing their joint probability distribution. Through rigorous probabilistic modeling and statistical analysis, we derive an analytical characterization of the joint distribution of multi-model outputs. This enables, for the first time, systematic and unified quantification of both model and input uncertainties at the system level. The framework establishes a principled foundation for high-reliability decision-making, robust system design, and subsequent uncertainty propagation algorithms.
📝 Abstract
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.