# Doubly Robust Estimation of Causal Effect on CVR with Targeted Regularization

arXiv: https://arxiv.org/abs/2608.13461 · HTML: https://mlsanity.com/paper/2608.13461/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 44 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 20 of 20)

- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Entire Space Multi-Task Model: An Effective Approach for Estimating Post-Click Conversion Rate](https://mlsanity.com/paper/1804.07931/) (2018)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [Estimating the Effects of Continuous-valued Interventions using Generative Adversarial Networks](https://mlsanity.com/paper/2002.12326/) (2020)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [Nonparametric methods for doubly robust estimation of continuous treatment effects](https://mlsanity.com/paper/1507.00747/) (2015)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Counterfactual Representation Learning with Balancing Weights](https://mlsanity.com/paper/2010.12618/) (2020)
- [Learning Weighted Representations for Generalization Across Designs](https://mlsanity.com/paper/1802.08598/) (2018)
- [Large-scale Causal Approaches to Debiasing Post-click Conversion Rate Estimation with Multi-task Learning](https://mlsanity.com/paper/1910.09337/) (2019)
- [Explicit Feature Interaction-aware Uplift Network for Online Marketing](https://mlsanity.com/paper/2306.00315/) (2023)
- [Doubly Robust Causal Effect Estimation under Networked Interference via Targeted Learning](https://mlsanity.com/paper/2405.03342/) (2024)
- [A Generalized Doubly Robust Learning Framework for Debiasing Post-Click Conversion Rate Prediction](https://mlsanity.com/paper/2211.06684/) (2022)
- [A Large Scale Benchmark for Individual Treatment Effect Prediction and Uplift Modeling](https://mlsanity.com/paper/2111.10106/) (2021)
- [Adversarially Balanced Representation for Continuous Treatment Effect Estimation](https://mlsanity.com/paper/2312.10570/) (2023)
- [Entire Chain Uplift Modeling with Context-Enhanced Learning for Intelligent Marketing](https://mlsanity.com/paper/2402.03379/) (2024)

## Abstract (arXiv)

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.