Doubly Robust Estimation of Causal Effect on CVR with Targeted Regularization

2026-08-13

AI Summary

This work addresses the selection bias and high variance inherent in causal estimation of post-click conversion rates (CVR), which arise from reliance solely on clicked samples. Drawing on semiparametric theory, the authors propose the first doubly robust estimator tailored to chain-structured outcomes and incorporate outcome regularization to enhance numerical stability. The method remains consistent even when nuisance parameters are misspecified and achieves a faster convergence rate than existing approaches. Theoretical analysis further reveals fundamental limitations in naively debiasing composite losses or directly applying standard causal estimators. Empirical results demonstrate that the proposed estimator significantly outperforms current baselines on both synthetic and real-world datasets, exhibiting strong effectiveness and robustness.

Abstract

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.

Problem

• Causal Effect
• Conversion Rate
• Sample Selection Bias
• Doubly Robust Estimation
• Post-click CVR

Innovation

• doubly robust estimation
• post-click conversion rate
• targeted regularization
• semiparametric theory
• causal inference