  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.
