  The Lasso has become a benchmark data analysis procedure, and numerous
variants have been proposed in the literature. Although the Lasso formulations
are stated so that overall prediction error is optimized, no full control over
the accuracy prediction on certain individuals of interest is allowed. In this
work we propose a novel version of the Lasso in which quadratic performance
constraints are added to Lasso-based objective functions, in such a way that
threshold values are set to bound the prediction errors in the different groups
of interest (not necessarily disjoint). As a result, a constrained sparse
regression model is defined by a nonlinear optimization problem. This
cost-sensitive constrained Lasso has a direct application in heterogeneous
samples where data are collected from distinct sources, as it is standard in
many biomedical contexts. Both theoretical properties and empirical studies
concerning the new method are explored in this paper. In addition, two
illustrations of the method on biomedical and sociological contexts are
considered.
