Doubly Robust Estimation of Causal Effect on CVR with Targeted Regularization

Post-click conversion rate (CVR) is a key metric in various scenarios including e-commerce and advertising, reflecting the efficiency and user experience in the second stage of the conversion process. Estimating the causal effect on CVR is therefore of great practical importance. However, directly applying existing causal inference methods to clicked samples introduces sample selection bias and increased variance due to the exclusion of non-click data. Recent studies on CVR prediction introduce "ideal loss", which optimizes model parameters using an unbiased estimate of the loss over the full sample. Nevertheless, there is no guarantee that unbiasedness of the loss implies unbiasedness of the final estimator. We revisit this challenge from the perspective of semiparametric theory. Specifically, we develop a new doubly robust causal effect estimator for chain-structured outcomes such as CVR, and derive its theoretical properties in detail. It achieves a faster convergence rate compared to nuisance parameters estimation and is therefore more robust when using flexible nonparametric estimators, including neural networks. Based on these theoretical findings, we further design a framework based on targeted regularization to improve numerical stability and practical applicability. Extensive experiments on synthetic and real-world data demonstrate the effectiveness and robustness of our method. In addition, we find that naively combining loss debiasing with standard causal estimators underperforms our method, highlighting the necessity of developing the new estimator tailored to this CVR-style objective with solid theoretical guarantees.

Treatment Effect Estimation for Exponential Family Outcomes using Neural Networks with Targeted Regularization

Neural Networks (NNs) have became a natural choice for treatment effect estimation due to their strong approximation capabilities. Nevertheless, how to design NN-based estimators with desirable properties, such as low bias and doubly robustness, still remains a significant challenge. A common approach to address this is targeted regularization, which modifies the objective function of NNs. However, existing works on targeted regularization are limited to Gaussian-distributed outcomes, significantly restricting their applicability in real-world scenarios. In this work, we aim to bridge this blank by extending this framework to the boarder exponential family outcomes. Specifically, we first derive the von-Mises expansion of the Average Dose function of Canonical Functions (ADCF), which inspires us how to construct a doubly robust estimator with good properties. Based on this, we develop a NN-based estimator for ADCF by generalizing functional targeted regularization to exponential families, and provide the corresponding theoretical convergence rate. Extensive experimental results demonstrate the effectiveness of our proposed model.