Automatic uncertainty evaluation for determining the number of components in nested models and the shrinkage regularization parameters

In this study, we propose and examine two procedures for constructing intervals that capture the uncertainty associated with determining the effective number of components in model selection problems or the shrinkage parameters in a regularization problem. The output of these methods is an interval (defined by two integer bounds) representing plausible values for the number of components and/or shrinkage parameters. Notably, these methods do not rely on the availability of a likelihood function, making them broadly applicable across various domains, such as regression, classification, feature and/or order selection, clustering, and dimensionality reduction. These techniques leverage the geometric properties of the error curve to construct intervals. Extensive experiments on both synthetic and real-world datasets demonstrated the effectiveness and practical utility of the proposed procedures. In addition, a MATLAB code is provided to facilitate adoption by practitioners and researchers.