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Unveiling the Potential of Robustness in Selecting Conditional Average Treatment Effect Estimators

Yiyan Huang, Cheuk Hang Leung, Siyi Wang, Yijun Li, Qi Wu

TL;DR

The proposed DRM is nuisance-free, eliminating the need to fit models for nuisance parameters, and it effectively prioritizes the selection of a distributionally robust CATE estimators that are robust to the distribution shift incurred by covariate shift and hidden confounders.

Abstract

The growing demand for personalized decision-making has led to a surge of interest in estimating the Conditional Average Treatment Effect (CATE). Various types of CATE estimators have been developed with advancements in machine learning and causal inference. However, selecting the desirable CATE estimator through a conventional model validation procedure remains impractical due to the absence of counterfactual outcomes in observational data. Existing approaches for CATE estimator selection, such as plug-in and pseudo-outcome metrics, face two challenges. First, they must determine the metric form and the underlying machine learning models for fitting nuisance parameters (e.g., outcome function, propensity function, and plug-in learner). Second, they lack a specific focus on selecting a robust CATE estimator. To address these challenges, this paper introduces a Distributionally Robust Metric (DRM) for CATE estimator selection. The proposed DRM is nuisance-free, eliminating the need to fit models for nuisance parameters, and it effectively prioritizes the selection of a distributionally robust CATE estimator. The experimental results validate the effectiveness of the DRM method in selecting CATE estimators that are robust to the distribution shift incurred by covariate shift and hidden confounders.

Unveiling the Potential of Robustness in Selecting Conditional Average Treatment Effect Estimators

TL;DR

The proposed DRM is nuisance-free, eliminating the need to fit models for nuisance parameters, and it effectively prioritizes the selection of a distributionally robust CATE estimators that are robust to the distribution shift incurred by covariate shift and hidden confounders.

Abstract

The growing demand for personalized decision-making has led to a surge of interest in estimating the Conditional Average Treatment Effect (CATE). Various types of CATE estimators have been developed with advancements in machine learning and causal inference. However, selecting the desirable CATE estimator through a conventional model validation procedure remains impractical due to the absence of counterfactual outcomes in observational data. Existing approaches for CATE estimator selection, such as plug-in and pseudo-outcome metrics, face two challenges. First, they must determine the metric form and the underlying machine learning models for fitting nuisance parameters (e.g., outcome function, propensity function, and plug-in learner). Second, they lack a specific focus on selecting a robust CATE estimator. To address these challenges, this paper introduces a Distributionally Robust Metric (DRM) for CATE estimator selection. The proposed DRM is nuisance-free, eliminating the need to fit models for nuisance parameters, and it effectively prioritizes the selection of a distributionally robust CATE estimator. The experimental results validate the effectiveness of the DRM method in selecting CATE estimators that are robust to the distribution shift incurred by covariate shift and hidden confounders.
Paper Structure (41 sections, 12 theorems, 76 equations, 1 figure, 3 tables, 1 algorithm)

This paper contains 41 sections, 12 theorems, 76 equations, 1 figure, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Challenge 1: How to determine the metric form and underlying ML models for nuisance parameters?
  3. Challenge 2: These metrics are not well-targeted for selecting robust a CATE estimator.
  4. Contributions.
  5. Background of CATE Estimator Selection
  6. Related Work
  7. CATE estimation.
  8. CATE estimator selection.
  9. The Distributionally Robust Metric
  10. Capturing the Uncertainty in PEHE
  11. Establishing Distributionally Robust Metric
  12. Step 1: Establishing computational tractability of $\mathcal{V}^t(\hat{\tau})$.
  13. Step 2: Finalizing Distributionally Robust Metric for CATE estimator selection.
  14. Discussion on the ambiguity radius $\epsilon$.
  15. Experiments
  16. ...and 26 more sections

Key Result

Proposition 4.1

The PEHE w.r.t. the CATE estimator $\hat{\tau}$ can be decomposed as follows: where $\zeta = \mathbb{E}[(\mu_1(X)-\mu_0(X))^2]$. The proof is deferred to Appendix app:proof_pehe_decompose.

Figures (1)

  • Figure 1: The stacked bar chart showing the distribution of the selected estimator's rank for each evaluation metric across rank intervals: [1-3], [4-11], [12-19], [20-27], and [28-36]. The greener (or redder) color indicates that the selected estimator ranks higher (or lower). For example, the dark red (or green) indicates the percentage of cases (out of 100 experiments) where the selected estimator ranks among the worst 9 estimators, specifically as ranks 28, 29, ..., or 36 (or among the best 3 estimators, specifically as ranks 1, 2, or 3).

Theorems & Definitions (22)

  • Proposition 4.1
  • Definition 4.2: KL ambiguity set
  • Corollary 4.3
  • Theorem 4.4
  • Theorem 4.5
  • Proposition 4.6
  • proof
  • Proposition B.1
  • proof
  • proof
  • ...and 12 more