Pliable lasso for the support vector machine

In this article, we study the support vector machine with interaction effects. The pliable lasso penalty, which allows for estimating the main effects of the covariates X and the interaction effects between the covariates and a set modifiers Z is implemented to handle the interaction effect. Interaction variables are included in a hierarchical manner by first considering whether their corresponding main effect variables have been included in the model to avoid over-fitting. The loss function employed is the squared hinge loss, with the pliable lasso penalty and then, the block-wise coordinate descent approach is employed. The results from the simulation and real data show the effectiveness of the pliable lasso in building support vector machine models in situations where interaction effects are involved.