Projection predictive variable selection for discrete response families with finite support

Understand

The projection predictive variable selection is a decision-theoretically justified Bayesian variable selection approach achieving an outstanding trade-off between predictive performance and sparsity.

• Its projection problem is not easy to solve in general because it is based on the Kullback-Leibler divergence from a restricted posterior predictive distribution of the so-called reference model to the parameter-conditional predictive distribution of a candidate model.
• Previous work showed how this projection problem can be solved for response families employed in generalized linear models and how an approximate latent-space approach can be used for many other response families.
• Here, we present an exact projection method for all response families with discrete and finite support, called the augmented-data projection.