Machine learning (ML) models are increasingly being used in metrology
applications. However, for ML models to be credible in a metrology context they
should be accompanied by principled uncertainty quantification. This paper
addresses the challenge of uncertainty propagation through trained/fixed
machine learning (ML) regression models. Analytical expressions for the mean
and variance of the model output are obtained/presented for certain input data
distributions and for a variety of ML models. Our results cover several popular
ML models including linear regression, penalised linear regression, kernel
ridge regression, Gaussian Processes (GPs), support vector machines (SVMs) and
relevance vector machines (RVMs). We present numerical experiments in which we
validate our methods and compare them with a Monte Carlo approach from a
computational efficiency point of view. We also illustrate our methods in the
context of a metrology application, namely modelling the state-of-health of
lithium-ion cells based upon Electrical Impedance Spectroscopy (EIS) data

机器学习模型在计量学应用中的可信度需要伴随确定性不确定性的量化，本文解决了经过训练 / 固定的机器学习回归模型中不确定性传播的挑战，提供了在特定输入数据分布和多种机器学习模型下，对模型输出均值和方差的解析表达式，并通过数值实验验证方法，与蒙特卡罗方法在计算效率上进行比较，同时以锂离子电池状态建模为例，展示了方法的应用。