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Generalization Bounds for Causal Regression: Insights, Guarantees and Sensitivity Analysis
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Derives finite-sample generalization bounds for causal regression (outcome regression, T/S/X-learners) via a Pearson chi-square change-of-measure inequality with a tunable lambda, yielding empirically computable bounds robust to hidden confounding and positivity violations.
Problem
Lack of finite-sample theory for causal regression algorithms (outcome regression and individual treatment effect estimation); existing bounds are loose and restricted to MSE and pseudo-VC dimension, and assume ignorability/positivity.
Approach
A change-of-measure inequality based on Pearson chi-square divergence with a tuning parameter lambda (recovering equality as lambda grows when P=Q), applied to reweighted empirical risk to bound the unobservable counterfactual loss; the chi-square term is relaxed via a Brier score of an arbitrary propensity model plus a balance term, making it empirically boundable.
Key results
- The theoretical bound closely matches the unobservable complete loss in near-RCT and hidden-confounding settings, while the prior bound is multiple orders of magnitude looser.
- Optimizing the lambda parameter makes the bounds over 30x tighter than the lambda=1 choice used in prior change-of-measure bounds.
- On Parkinson's telemonitoring, bounds show Random Forest T/S-learners no longer clearly outperform gradient boosting meta-learners once the observed-to-complete gap is accounted for.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed theoretical bound instead of the closest prior-work bound | Potential-outcome regression loss bounds · Learned IHDP, ACIC16, and Confounded ACIC16 | bound tightness: multiple orders of magnitude looser | Helped |
| Optimize the tuning parameter λ rather than fixing it at 1 | Change-of-measure bound · Confounded ACIC16 | bound tightness: over 30$\times$ tighter | Helped |
| Use the theoretical bound on the Near-RCT data | Potential-outcome regression loss · Learned IHDP (Near-RCT) | bound tightness | Helped |
| Use the theoretical bound with hidden confounding | Potential-outcome regression loss · Confounded ACIC16 | bound tightness | Helped |
| Use the empirical bound rather than the theoretical bound | Potential-outcome regression loss · Confounded ACIC16 | bound tightness | Hurt |
| Use the proposed bounds on observational data with fully observed confounding | Potential-outcome regression loss · ACIC16 | bound tightness | Mixed |
| Apply the proposed bounds when selecting models | Treatment-effect meta-learners · Parkinson's Telemonitoring | complete treatment-effect loss | Mixed |
| Use Random Forest-backed T- or S-learners instead of linear meta-learners | Treatment-effect meta-learners · Parkinson's Telemonitoring | complete treatment-effect loss | Helped |
| Use an X-learner instead of a Random Forest T- or S-learner | Treatment-effect meta-learners · Parkinson's Telemonitoring | observable loss | Hurt |
Surprising findings
- Quantile treatment effects can be estimated by a T-learner trained with quantile loss, even though quantile of the difference is not the difference of quantiles in general; the bound controls the complete quantile loss but convergence is not proven.
- Empirical bounds are exceptionally tight in the hidden confounding setting, possibly because positivity is violated.
Limitations
- Relaxed empirical bound is looser than the theoretic bound because of the triangle-inequality relaxation and balance term D.
- Bounds do not account for interactions between the component regressions h1 and h0 in meta-learners.
- Variance of loss must be conservatively bounded by hand in the real-data application; the weight maximum can make finite-sample terms large.
Experimental setup
Datasets: IHDP ACIC16 Parkinson's Telemonitoring
Benchmarks: Learned IHDP ACIC16 Confounded ACIC16 Parkinson's Telemonitoring
Metrics: complete loss bound tightness observed loss bootstrapped confidence intervals
Baselines: prior pseudo-VC/IPM-based generalization bound (Corollary 1 of the cited prior w Lasso gradient boosting random forest
Builds on: T-learner S-learner X-learner Rademacher complexity bounds
Closest papers by meaning
- Estimating individual treatment effect: generalization bounds and algorithms (ICML 2017 · similarity 0.87)
- Do causal predictors generalize better to new domains? (NeurIPS 2024 · similarity 0.86)
- Which Algorithms Have Tight Generalization Bounds? (NeurIPS 2025 · similarity 0.86)
- Generalized Bayes for Causal Inference (NeurIPS 2026 · similarity 0.86)
- Prediction-powered Generalization of Causal Inferences (ICML 2024 · similarity 0.86)
- Certification-Enhanced Generalization Bounds (NeurIPS 2026 · similarity 0.86)
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