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Bounds on Representation-Induced Confounding Bias for Treatment Effect Estimation
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Proposes a representation-agnostic neural refutation framework that uses a marginal sensitivity model to estimate lower and upper bounds on representation-induced confounding bias in representation-learning CATE estimators.
Problem
Low-dimensional or constrained representations used in representation-learning CATE estimation lose confounder information, inducing confounding bias so CATE becomes non-identifiable from representations; validity of such estimators is violated.
Approach
Treat the representation-induced confounding bias as a partial identification problem: use the marginal sensitivity model with sensitivity parameters estimated from data (no unobserved confounding), and compute bounds via conditional normalizing flows and CVaR-style integrals, then defer decisions inside the bounds.
Key results
- On the synthetic benchmark with d_phi=1, the bounds reduce TARNet's out-sample policy error rate from 30.79% to about 17.9% (a 12.89 point reduction).
- On IHDP100 with d_phi=5, the bounds reduce TARNet's error rate from 3.17% by 2.65 points, and they improve error for almost all baselines.
- On HC-MNIST with d_phi=7, the bounds reduce CFR (WM; alpha=1.0) error from 24.55% by 10.42 points.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use bounds-based decisions with deferral instead of point-estimate decisions | Representation-learning CATE methods · Synthetic, dφ=1 | out-sample policy error rate: −12.89% | Helped |
| Use bounds-based decisions with deferral instead of point-estimate decisions | Representation-learning CATE methods · Synthetic, dφ=2 | out-sample policy error rate: −0.02% | Helped |
| Use bounds-based decisions with deferral instead of point-estimate decisions | Representation-learning CATE methods · HC-MNIST, dφ=7 | out-sample policy error rate: −2.59%; −10.42%; +19.25% | Mixed |
| Use bounds-based decisions with deferral instead of point-estimate decisions | Representation-learning CATE methods · HC-MNIST, dφ=39 | out-sample policy error rate: −3.34% | Helped |
| Use bounds-based decisions with deferral instead of point-estimate decisions | Representation-learning CATE methods · HC-MNIST, dφ=78 | out-sample policy error rate: −2.62% | Helped |
| Use bounds-based decisions with deferral instead of point-estimate decisions | Representation-learning CATE methods · IHDP100 | out-sample policy error rate: −0.89%; +3.98%; +1.89%; +6.37% | Mixed |
| Increase CFR MMD balancing coefficient from α=0.1 to α=0.5 | CFR · IHDP100, dφ=10 | out-sample policy error rate: −1.03% -> +3.98% | Hurt |
Surprising findings
- Refutation bounds sometimes worsen error rates, e.g., CFR (MMD; alpha=0.5) on IHDP100 and CFR (MMD; alpha=0.5) on HC-MNIST with d_phi=7 (+19.25%).
Limitations
- Bounds are conservative: they widen when information about the instruments is lost even if no RICB arises.
- Sensitivity parameter depends on delta-ball hyperparameter, which only affects conservativeness.
- Relies on estimated propensity and conditional density models; results depend on their quality.
Experimental setup
Datasets: synthetic confounding benchmark IHDP100 HC-MNIST MNIST
Benchmarks: synthetic benchmark IHDP100 HC-MNIST
Metrics: out-sample policy error rate deferral rate rPEHE
Baselines: TARNet BNN CFR InvTARNet RCFR CFR-ISW BWCFR k-NN BART C-Forest
Builds on: TARNet CFR marginal sensitivity model CFR-ISW BWCFR
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