  Despite the growing popularity of machine-learning techniques in
decision-making, the added value of causal-oriented strategies with respect to
pure machine-learning approaches has rarely been quantified in the literature.
These strategies are crucial for practitioners in various domains, such as
marketing, telecommunications, health care and finance. This paper presents a
comprehensive treatment of the subject, starting from firm theoretical
foundations and highlighting the parameters that influence the performance of
the uplift and predictive approaches. The focus of the paper is on a binary
outcome case and a binary action, and the paper presents a theoretical analysis
of uplift modeling, comparing it with the classical predictive approach. The
main research contributions of the paper include a new formulation of the
measure of profit, a formal proof of the convergence of the uplift curve to the
measure of profit ,and an illustration, through simulations, of the conditions
under which predictive approaches still outperform uplift modeling. We show
that the mutual information between the features and the outcome plays a
significant role, along with the variance of the estimators, the distribution
of the potential outcomes and the underlying costs and benefits of the
treatment and the outcome.
