A New Transformation Approach for Uplift Modeling with Binary Outcome

TL;DR

The paper tackles uplift modeling for binary outcomes, where traditional transformed-outcome methods often fail to efficiently use the treatment indicator when the outcome is zero. It introduces a novel transformed outcome, $\hat{Z}^* = (Y - C)\frac{W - p(X)}{p(X)(1 - p(X))}$ with $0<C<1$, ensuring $\mathbb{E}[\hat{Z}^*|X]=\tau(x)$ under unconfoundedness and enabling standard learners to estimate uplift more effectively. Empirical results on synthetic data and a large real-world marketing campaign demonstrate that $\hat{Z}^*$ consistently improves uplift metrics such as $Qini$ and $AUUC$, especially in low-response settings and at the top end of the uplift distribution. The findings support the method's practical utility for precision marketing and similar applications where binary outcomes are prevalent and sample efficiency matters.

Abstract

Uplift modeling has been used effectively in fields such as marketing and customer retention, to target those customers who are more likely to respond due to the campaign or treatment. Essentially, it is a machine learning technique that predicts the gain from performing some action with respect to not taking it. A popular class of uplift models is the transformation approach that redefines the target variable with the original treatment indicator. These transformation approaches only need to train and predict the difference in outcomes directly. The main drawback of these approaches is that in general it does not use the information in the treatment indicator beyond the construction of the transformed outcome and usually is not efficient. In this paper, we design a novel transformed outcome for the case of the binary target variable and unlock the full value of the samples with zero outcome. From a practical perspective, our new approach is flexible and easy to use. Experimental results on synthetic and real-world datasets obviously show that our new approach outperforms the traditional one. At present, our new approach has already been applied to precision marketing in a China nation-wide financial holdings group.

Figures (2)

• Figure 1: Model performance in Qini Curve of different approaches ($Z$, $Z^*$ and $\hat{Z}^*$) for synthetic dataset with high (LEFT) and low (RIGHT) response rate.
• Figure 2: Model performance in cumulative uplift of old approach $Z^*$ (LEFT) and new approach $\hat{Z}^*$ (RIGHT) for a real world marketing campaign.

Theorems & Definitions (1)

• proposition 1