  Many problems in statistics and machine learning can be formulated as model
selection problems, where the goal is to choose an optimal parsimonious model
among a set of candidate models. It is typical to conduct model selection by
penalizing the objective function via information criteria (IC), as with the
pioneering work by Akaike and Schwarz. Via recent work, we propose a
generalized IC framework to consistently estimate general loss-based learning
problems. In this work, we propose a consistent estimation method for
Generalized Linear Model (GLM) regressions by utilizing the recent IC
developments. We advance the generalized IC framework by proposing model
selection problems, where the model set consists of a potentially uncountable
set of models. In addition to theoretical expositions, our proposal introduces
a computational procedure for the implementation of our methods in the finite
sample setting, which we demonstrate via an extensive simulation study.
