How Correlations Influence Lasso Prediction

Mohamed Hebiri, Johannes Lederer

Abstract: We study how correlations in the design matrix influence Lasso prediction. First, we argue that the higher the correlations, the smaller the optimal tuning parameter. This implies in particular that the standard tuning parameters, that do not depend on the design matrix, are not favorable. Furthermore, we argue that Lasso prediction works well for any degree of correlations if suitable tuning parameters are chosen. We study these two subjects theoretically as well as with simulations.