Bayesian Semi-Supervised Learning (BSSL) for spectral variable selection.

Variable selection are increasingly developed and deployed in spectra analysis, ensuring their reliability has become crucial. However, external disturbances during spectrum measurement, such as noise and distribution shifts, can introduce uncertainties that challenge the reliability of variable selection. To address these challenges, a Bayesian Semi-Supervised Learning (BSSL) framework for variable selection and model updating was developed. First, we propose a Bayesian variable selection method based on maximum likelihood estimation (MLE) and posterior variance, which assesses variable uncertainty by probabilistic framework. Second, we develop a semi-supervised learning framework that incorporates unlabeled target samples for model adaptation. A pseudo-labeling update strategy is employed, allowing neighboring variables to be adjusted, thereby enhancing the model's performance on the target dataset. Extensive experiments on publicly available datasets validate the effectiveness of the proposed algorithm. Moreover, the selected variables consistently align with the sensitive spectral regions associated with the target analytes, and updates tend to occur in neighboring regions. These results not only indicate the enhanced predictive performance but also prove the interpretability and robustness of the method.