Lasso type classifiers with a reject option

This paper discusses structural risk minimization in the setting of classification with a reject option. Binary classification is about classifying observations that take values in an arbitrary feature space X into one of two classes, labelled −1 or +1. A discriminant function f : X → R yields a classifier sgn(f(x)) ∈ {−1,+1} that represents our guess of the label Y of a future observation X and we err if the margin y · f(x) < 0. Since observations x for which the conditional probability