Addressing Nonnegligible Model Uncertainty in Machine Learning-Assisted Measurements

Machine learning (ML) techniques are increasingly used in measurement science to develop novel measurement models. Such ML-based measurement models are particularly useful when conventional ones are unavailable, enabling measurement operations that would otherwise be impractical. However, the resulting relationship between the measurand and the input quantities is not directly selected by the practitioner; rather, it is inherently determined by a data-driven training process. This gives rise to an additional uncertainty component (denoted in previous work as measurement-model uncertainty) which, when adherence to the Joint Committee for Guides in Metrology (JCGM) is required, shall be negligible with respect to the component associated with the measurement of the physical input quantities (denoted in previous work as physical quantity uncertainty). When this condition cannot be met, a direct application of the JCGM framework may understate the measurement uncertainty, thereby yielding coverage intervals that are not representative of the values that can be reasonably attributed to the measurand. Accordingly, to address the limitations of a direct JCGM application while remaining consistent with its framework, this work proposes a JCGM-compliant method that leverages joint probability distributions, sampled via nested Monte Carlo simulations, to obtain a fully fledged measurement result for ML-assisted measurements. Two illustrative case studies based on deterministic ML regressors demonstrate the applicability of the proposed method and show that the resulting coverage intervals explicitly account for the variability introduced by the ML model, thereby avoiding any understatement of the reported measurement uncertainty.