Analytical results for uncertainty propagation through trained machine learning regression models.

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 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. • Novel analytical results for uncertainty propagation through kernel-based models. • Our methods offer an alternative to Monte Carlo sampling approaches. • Benefits include greater accuracy, transparency and reproducibility. • The computational efficiency of analytical and Monte Carlo approaches is compared. • We illustrate our methods on state-of-health modelling of lithium-ion cells. [ABSTRACT FROM AUTHOR]