Székely Regularization for Uplift Modeling

Abstract

Uplift modeling is a subfield of machine learning concerned with predicting the causal effect of an action at the level of individuals. This is achieved by using two training sets: treatment, containing objects which have been subjected to an action and control, containing objects on which the action has not been performed. An uplift model then predicts the difference between conditional success probabilities in both groups. Uplift modeling is best applied to training sets obtained from randomized controlled trials, but such experiments are not always possible, in which case treatment assignment is often biased. In this paper we present a modification of Uplift Support Vector Machines which makes them less sensitive to such a bias. This is achieved by including in the model formulation an additional term which penalizes models which score treatment and control groups differently. We call the technique Székely regularization since it is based on the energy distance proposed by Székely and Rizzo. Optimization algorithm based on stochastic gradient descent techniques has also been developed. We demonstrate experimentally that the proposed regularization term does indeed produce uplift models which are less sensitive to biased treatment assignment.