Stable lasso for model structure learning of inferential sensor modeling

In this paper, we propose a stabilization strategy for lasso to use cross-validation (CV) for structure learning. It is known that cross-validation often prefers very small λ that selects an excessively large number of variables, which is also in a less stable region of λ. In this paper, we propose to reduce the heterogeneity of the model structures during the CV step. We first build a series of models using all data with a grid of λ. Then the models of all CV-folds use a revised lasso objective that penalizes deviations from the model structure using all data. Further, we propose a stable selection criterion that uses CV prediction errors jointly with a stability measure to select the most stable model with near minimum CV errors. The proposed strategy is demonstrated using data from an industrial boiler process to predict NOx emissions.