I was reading about stability selection applied to LASSO. My understanding is that stability selection (Meinshausen & Buhlman, 2010) helps in finding stable variables, with error control provided by an upper bound, but it doesn't provide an optimized regularisation parameter, so I'd say that it doesn't really do model selection. I see how using only the subset of stable variables identified in this way to train further models might be wrong. So my question is how feature selection performed with stability can be integrated in a predictive framework?
Imagine I have a classification problem with binary outcome. I am interested in assessing the prediction performance of LASSO and identify stable predictors and their sign (association with the outcome).
The only way I see is to perform a LASSO using, for instance, a nested k-fold cross-validation and evaluate model performance.
Then perform stability selection as a separate analysis to identify significant predictors. I expect that the subset of variables selected in each loop of the nested cv will be, at least, slightly different from the stable variables identified by stability selection. My question is, is it ok to evaluate model performance with a metod and predictors importance with another method? Is there a way to extract coefficient signs from stability selection procedure (I'm using stabsel in R).