Uncertainty calibration for latent-variable regression models

Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression models (partial least-squares regression, PLS, principal component regression, PCR) along with their kernelized versions (kernel partial least-squares regression, K-PLS, kernel principal component regression, K-PCR), do not incorporate uncertainty quantification as part of their output. In this study, we propose a method inspired by conformal inference to estimate and calibrate the uncertainty of multivariate statistical models. The result of this method is a point prediction accompanied by prediction intervals that depend on the input data. We tested the proposed method on both traditional and kernelized versions of PLS and PCR. The method is demonstrated using synthetic data, as well as laboratory near-infrared (NIR) and airborne hyperspectral regression models for estimating functional plant traits. The model was able to successfully identify the uncertain regions in the simulated data and match the magnitude of the uncertainty. In real-case scenarios, the optimised model was not overconfident nor underconfident when estimating from test data: for example, for a 95% prediction interval, 95% of the true observations were inside the prediction interval.