An Uncertainty-Aware Kernel-Based Method: The Generalized Least Squares Support Vector Machines

A robust evaluation of predictive uncertainty is essential for deploying machine learning models in high-risk sectors. While various techniques such as Gaussian Processes and Bayesian Neural Networks have been developed to address model uncertainty, the measurement uncertainty associated with input data, particularly regarding heteroscedasticity and autocorrelation, is often overlooked. This work introduces the Generalized Least Squares Support Vector Machines (GLS-SVM), a kernel-based regression model designed to integrate the full variance-covariance matrix of the response variable into the training process. A GUM-consistent methodology is then developed for evaluating prediction uncertainty including a correction for model bias. The performance of the proposed model is validated using two case studies: a simulated regression problem with heteroscedastic, autocorrelated noise and the calibration of a mass flow controller. Results demonstrate that GLS-SVM significantly outperforms other kernel-based models when dealing with correlated data, providing accurate estimations and physically consistent standard uncertainties. This approach offers a versatile, metrologically-informed framework for data-driven regression tasks where measurement covariance information is available and rigorous uncertainty quantification is required.