The predictive Lasso

We propose a shrinkage procedure for simultaneous variable selection and estimation in generalized linear models (GLMs) with an explicit predictive motivation. The procedure estimates the coefficients by minimizing the Kullback-Leibler divergence of a set of predictive distributions to the corresponding predictive distributions for the full model, subject to an l 1 constraint on the coefficient vector. This results in selection of a parsimonious model with similar predictive performance to the full model. Thanks to its similar form to the original Lasso problem for GLMs, our procedure can benefit from available l 1-regularization path algorithms. Simulation studies and real data examples confirm the efficiency of our method in terms of predictive performance on future observations