Identifying a Minimal Class of Models for High--Dimensional Data

Abstract

Model selection consistency in the high--dimensional regression setting can be achieved only if strong assumptions are fulfilled. We therefore suggest to pursue a different goal, which we call a minimal class of models. The minimal class of models includes models that are similar in their prediction accuracy but not necessarily in their elements. We suggest a random search algorithm to reveal candidate models. The algorithm implements simulated annealing while using a score for each predictor that we suggest to derive using a combination of the lasso and the elastic net. The utility of using a minimal class of models is demonstrated in the analysis of two data sets.