Analytical results for uncertainty propagation through trained machine learning regression models
This work addresses the need for principled uncertainty quantification in metrology applications, such as modeling lithium-ion cell health, to enhance the credibility of ML models in scientific and industrial settings.
The paper tackles the challenge of uncertainty propagation through trained machine learning regression models by deriving analytical expressions for the mean and variance of model outputs for specific input distributions and various ML models, including linear regression, kernel ridge regression, and Gaussian Processes, and validates these methods with numerical experiments showing computational efficiency gains compared to Monte Carlo approaches.
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