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# Causal Inference and Uplift Modelling: A Review of the Literature

*Proceedings of The 3rd International Conference on Predictive Applications and APIs*, PMLR 67:1-13, 2017.

#### Abstract

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 difficult 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 effect estimator is equivalent to minimizing the MSE in which the unobserved treatment effect 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.