  For regulatory and interpretability reasons, logistic regression is still
widely used. To improve prediction accuracy and interpretability, a
preprocessing step quantizing both continuous and categorical data is usually
performed: continuous features are discretized and, if numerous, levels of
categorical features are grouped. An even better predictive accuracy can be
reached by embedding this quantization estimation step directly into the
predictive estimation step itself. But doing so, the predictive loss has to be
optimized on a huge set. To overcome this difficulty, we introduce a specific
two-step optimization strategy: first, the optimization problem is relaxed by
approximating discontinuous quantization functions by smooth functions; second,
the resulting relaxed optimization problem is solved via a particular neural
network. The good performances of this approach, which we call glmdisc, are
illustrated on simulated and real data from the UCI library and Cr\'edit
Agricole Consumer Finance (a major European historic player in the consumer
credit market).
