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Unveiling the Potential of Robustness in Selecting Conditional Average Treatment Effect Estimators
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Proposes DRM, a nuisance-free distributionally robust metric (KL ambiguity set) for selecting CATE estimators that are robust to covariate shift and hidden confounding, evaluated on semi-synthetic ACIC2016-based data against 13 baseline selectors.
Problem
Selecting a CATE estimator from observational data without counterfactual outcomes or ground-truth CATE; existing plug-in and pseudo-outcome selectors need nuisance models and do not target robustness to distribution shift.
Approach
Bounds the unobservable counterfactual PEHE terms with a KL-divergence ambiguity set centered on the factual distribution, derives a dual (log-sum-exp) form solved by Newton-Raphson, and sets the radius from covariate-distribution KL divergence, so no outcome, propensity or plug-in models are fit.
Key results
- DRM achieves the lowest regret in Setting A (0.96, 0.84, 1.25 across rho values) and Setting C (1.56, 1.40, 1.26 for m=0.1, 0.5, 0.9), where most baselines degrade.
- In Setting B with xi=2 (strong selection bias), DRM regret is 15.51 versus 5.91 for Plug-S/Plug-PS, so DRM underperforms there.
- DRM's rank correlation (about 0.80) is below Plug-S, Plug-PS, Plug-X and Plug-R (about 0.91-0.96), which the authors attribute to worst-case versus average-performance selection.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DRM instead of the strongest reported baseline selector | CATE estimator selection · Setting A (ρ=0, ρ=0.1, ρ=0.3) | Regret: 1.92 -> 0.96; 2.62 -> 0.84; 1.47 -> 1.25 | Helped |
| Use DRM instead of Plug-S | CATE estimator selection · Setting B (ξ=0) | Regret: 0.22 -> 0.38 | Hurt |
| Use DRM instead of Plug-S | CATE estimator selection · Setting B (ξ=2) | Regret: 5.91 -> 15.51 | Hurt |
| Use DRM instead of Plug-R | CATE estimator selection · Setting C (m=0.1, m=0.5, m=0.9) | Regret: 1.91 -> 1.56; 2.53 -> 1.40; 2.12 -> 1.26 | Helped |
| Use DRM for estimator ranking instead of Plug-R | CATE estimator selection · Settings A, B, and C | Spearman rank correlation: 0.96 -> 0.81; 0.96 -> 0.80; 0.96 -> 0.80; 0.95 -> 0.85; 0.93 -> 0.77; 0.96 -> 0.79; 0.96 -> 0.81; 0.96 -> 0.80 | Hurt |
Surprising findings
- DRM's ranking ability is weaker than several plug-in selectors, since worst-case robustness does not equal average ranking performance.
- The factual selection criterion performs better than DRM when there is no selection bias (xi=0).
Limitations
- Ambiguity radius is set heuristically from approximated covariate KL divergence and may not be optimal.
- Experiments are semi-synthetic with a limited CATE function complexity and a single data source (ACIC2016 covariates).
- Poor selection at strong selection bias (xi=2) and weaker rank correlation than several plug-in selectors.
Experimental setup
Datasets: ACIC2016 covariates (semi-synthetic)
Benchmarks: semi-synthetic ACIC2016-based settings A, B, C
Metrics: Regret Spearman rank correlation PEHE
Baselines: Plug-S Plug-T Plug-PS Plug-X Plug-U Plug-IPW Plug-DR Plug-R Plug-RA Pseudo-DR Pseudo-R Pseudo-IF
Builds on: Rubin causal model R-learner DR-learner X-learner Kullback-Leibler distributionally robust optimization
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