Qini-based Uplift Regression

Abstract

Uplift models provide a solution to the problem of isolating the marketing effect of a campaign. For customer churn reduction, uplift models are used to identify the customers who are likely to respond positively to a retention activity only if targeted, and to avoid wasting resources on customers that are very likely to switch to another company. We introduce a Qini-based uplift regression model to analyze a large insurance company's retention marketing campaign. Our approach is based on logistic regression models. We show that a Qini-optimized uplift model acts as a regularizing factor for uplift, much as a penalized likelihood model does for regression. This results in interpretable parsimonious models with few relevant explanatory variables. Our results show that performing Qini-based variable selection significantly improves the uplift models performance.

A Twin Neural Model for Uplift

“…Also, in practice, the R-learner is fitted in two stages using cross-fitting to emulate the oracle, thus requiring more observations than S-learners. The methodology introduced in Belbahri et al [2019] attacks parameters estimation and addresses the loss-metric mismatch in uplift regression. It can be seen as an S-learner which estimates the model's parameters in two stages.…”

“…Our goal is to regularize the conditional means in order to get a better prediction of the quantity of interest, the uplift. Inspired by the work of , Künzel et al [2019], Belbahri et al [2019], which adapt the optimization problem to the uplift context, we propose to define a composite loss function, which can be separated into two pieces:…”

“…This can be measured by the similarity between the theoretical uplift percentiles of predictions compared with empirical percentiles observed in the data. Maximizing the adjusted Qini coefficient, given in Definition 6, maximizes the Qini coefficient and simultaneously promotes grouping the individuals in decreasing uplift bins, which in turn result in concave Qini curves [Belbahri et al, 2019].…”

“…For fair comparison, we use the twin neural architecture. The second method is a two-stage method which is based on a derivative-free optimization of the qadj and imposes sparsity [Belbahri et al, 2019]. We denote this model by Qini-based and our proposed method by Twin µ .…”

“…(c) a Qini-based uplift regression model that uses several LHS structures to search for the optimal parameters (see Belbahri et al [2019] for more details). We denote this model by Qini-based.…”