DIGNet: Learning Decomposed Patterns in Representation Balancing for Treatment Effect Estimation
Abstract: Estimating treatment effects from observational data is often subject to a covariate shift problem incurred by selection bias. Recent research has sought to mitigate this problem by leveraging representation balancing methods that aim to extract balancing patterns from observational data and utilize them for outcome prediction. The underlying theoretical rationale is that minimizing the unobserved counterfactual error can be achieved through two principles: (I) reducing the risk associated with predicting factual outcomes and (II) mitigating the distributional discrepancy between the treated and controlled samples. However, an inherent trade-off between the two principles can lead to a potential loss of information useful for factual outcome predictions and, consequently, deteriorating treatment effect estimations. In this paper, we propose a novel representation balancing model, DIGNet, for treatment effect estimation. DIGNet incorporates two key components, PDIG and PPBR, which effectively mitigate the trade-off problem by improving one aforementioned principle without sacrificing the other. Specifically, PDIG captures more effective balancing patterns (Principle II) without affecting factual outcome predictions (Principle I), while PPBR enhances factual outcome prediction (Principle I) without affecting the learning of balancing patterns (Principle II). The ablation studies verify the effectiveness of PDIG and PPBR in improving treatment effect estimation, and experimental results on benchmark datasets demonstrate the superior performance of our DIGNet model compared to baseline models.
Submission Length: Long submission (more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=uyp8eFbzzT
Changes Since Last Submission: ## The revisions after the previous submission
We have made significant changes to the structure and content based on the constructive comments provided by the Reviewers and the Action Editor. Our revisions focus on improving the clarity and correctness of the paper. The key revisions can be summarized as follows:
1. Introduction: We have rewritten the Introduction section to clearly highlight our contributions, presenting them point by point. We have also added Figure 1, which visually illustrates the proposed components to improve readability.
2. Preliminaries: We have fixed some unclear points in notations and definitions.
3. Theoretical Results (Section 3): We have rewritten the content and scope of this section. Firstly, we provide the theoretical foundations of models without decomposed patterns, namely GNet and INet, before introducing them in Section 4. Secondly, to differentiate between previous results and our own contributions, we have divided Section 3 into two subsections: Section 3.1 focuses on the Wasserstein Distance Guided Error Bounds (theoretical foundation for GNet), while Section 3.2 discusses the $\mathcal{H}$-divergence Guided Error Bounds (theoretical foundation for INet).
4. Method (Section 4): We have restructured the Method section into two parts: Section 4.1, which covers Representation Balancing without Decomposed Patterns, and Section 4.2, which addresses Representation Balancing with Decomposed Patterns. In Section 4.1, we introduce GNet (Section 4.1.1) and INet (Section 4.1.2), corresponding to the theoretical results presented in Section 3.1 and Section 3.2, respectively. Particularly, Section 4.1.2 provides detailed explanations of how our derived Theorem 2 connects representation balancing with individual propensity confusion. In Section 4.2, we introduce the model DIGNet (Section 4.2.2) that learns decomposed patterns using the proposed methods PDIG and PPBR (Section 4.2.1).
5. Experiments (Section 5): We have revised the content and scope of the Experiments section. Firstly, we introduce three key questions at the beginning of Section 5 to suggest our goals. Additionally, we include two ablation models that are useful for conducting ablation studies. To aid comprehension, we also provide a diagram (Figure 2) illustrating the structures of the models compared in the ablation studies. In Section 5.1, we revise the paragraph of “Models and metrics”. Furthermore, we have added a significance analysis to investigate the statistical significance of the improvements in case the empirical results are overclaimed.
6. Conclusion (Section 6): We have added a paragraph “Limitations” to discuss potential areas for further research and acknowledge the limitations of our current study.
7. Appendix: We have removed redundant content from the Appendix and ensured that all the proofs and supplementary materials align with the content in the main paper."
## The revisions after the reviewers' feedback
We have made significant revisions based on the reviewers' insightful and constructive comments. The first-round revision is highlighted in red and the second-round revision is highlighted in blue. The changes are summarized as follows:
1. We rewrite most of the content of the Introduction to increase clarity and readability.
2. We provide a new motivating example better to illustrate the trade-off problem in causal representation learning.
3. We add more discussions on related works, including fair representation learning, trade-off problems in other machine learning research, and causal inference studies in different causal graph settings.
4. We add Section 4.3, which discusses some insights that help explain the effectiveness of our proposed method. Specifically, we demonstrate the extra thoughts on the improvements brought by PDIG and PPBR. Especially for PDIG, we give an example to discuss the differences between Wasserstein distance and H-divergence, and also demonstrate the need for incorporating both distance metrics. We also discuss the connection between our model and other machine learning methods.
5. We have made some minor revisions based on the reviewers' comments.
Supplementary Material: zip
Assigned Action Editor: ~Tom_Rainforth1
Submission Number: 1953
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