Thompson, A (2024) Analytical results for uncertainty propagation through trained machine learning regression models. Measurement, 234. 114841

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Abstract

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 wide 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 verify the correctness of 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.

Item Type:	Article
Subjects:	Mathematics and Scientific Computing > Measurement Uncertainties
Divisions:	Data Science
Identification number/DOI:	10.1016/j.measurement.2024.114841
Last Modified:	23 Sep 2024 12:14
URI:	https://eprintspublications.npl.co.uk/id/eprint/10051