Causal Inference and Uplift Modeling A review of the literature

Uplift modeling refers to the set of techniques used to model the incremental impact of an action or treatment on a customer outcome. Uplift modeling is therefore both a Causal Inference problem and a Machine Learning one. The literature on uplift is split into 3 main approaches–the Two-Model approach, the Class Transformation approach and modeling uplift directly. Unfortunately, in the absence of a common framework of causal inference and notation, it can be quite di cult to assess those three methods. In this paper, we use the Rubin (1974) model of causal inference and its modern “econometrics” notation to provide a clear comparison of the three approaches and generalize one of them. To our knowledge, this is the first paper that provides a unified review of the uplift literature. Moreover, our paper contributes to the literature by showing that, in the limit, minimizing the Mean Square Error (MSE) formula with respect to a causal e↵ect estimator is equivalent to minimizing the MSE in which the unobserved treatment e↵ect is replaced by a modified target variable. Finally, we hope that our paper will be of use to researchers interested in applying Machine Learning techniques to causal inference problems in a business context as well as in other fields: medicine, sociology or economics.