$$L_p$$Lp-Support vector machines for uplift modeling

Uplift modeling is a branch of machine learning which aims to predict not the class itself, but the difference between the class variable behavior in two groups: treatment and control. Objects in the treatment group have been subjected to some action, while objects in the control group have not. By including the control group, it is possible to build a model which predicts the causal effect of the action for a given individual. In this paper, we present a variant of support vector machines designed specifically for uplift modeling. The SVM optimization task has been reformulated to explicitly model the difference in class behavior between two datasets. The model predicts whether a given object will have a positive, neutral or negative response to a given action, and by tuning a parameter of the model the analyst is able to influence the relative proportion of neutral predictions and thus the conservativeness of the model. Further, we extend \(L_p\)-SVMs to the case of uplift modeling and demonstrate that they allow for a more stable selection of the size of negative, neutral and positive groups. Finally, we present quadratic and convex optimization methods for efficiently solving the two proposed optimization tasks.