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Quantifying Aleatoric Uncertainty of the Treatment Effect: A Novel Orthogonal Learner
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Proposes an orthogonal (Neyman-orthogonal) AU-learner for Makarov bounds on the conditional distribution of the treatment effect, with a conditional normalizing flow instantiation (AU-CNFs) for quantifying aleatoric uncertainty of treatment effects.
Problem
Quantifying aleatoric uncertainty of the individual treatment effect at the covariate-conditional level is needed for medical decisions, but the conditional distribution of the treatment effect (CDTE) is not point identifiable, and existing learners are plug-in estimators that are not orthogonal.
Approach
Derive the efficient influence function for Makarov bounds on the CDF/quantiles of the CDTE, use it for a gamma-scaled one-step bias correction of the covariate-adjusted loss yielding an orthogonal AU-learner (quasi-oracle efficient), and instantiate it with conditional normalizing flows.
Key results
- On HC-MNIST, AU-CNFs (CRPS) achieved the lowest out-sample rCRPS (0.347 upper, 0.357 lower) vs. 0.382/0.388 for CA-CNFs (CRPS).
- In synthetic experiments, AU-CNFs performed best in rCRPS in the majority of settings and training-set sizes.
- In low-sample settings, the CA-learner or plug-in approach sometimes performed nearly as well or better than the AU-learner.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the AU-learner with CRPS instead of the covariate-adjusted learner with CRPS | Conditional normalizing flows on HC-MNIST · HC-MNIST, upper bound | rCRPSout: 0.382 -> 0.347 | Helped |
| Use the AU-learner with CRPS instead of the covariate-adjusted learner with CRPS | Conditional normalizing flows on HC-MNIST · HC-MNIST, upper bound | W2 out: 1.029 -> 0.940 | Helped |
| Use the AU-learner with CRPS instead of the covariate-adjusted learner with CRPS | Conditional normalizing flows on HC-MNIST · HC-MNIST, lower bound | rCRPSout: 0.388 -> 0.357 | Helped |
| Use the AU-learner with CRPS instead of the covariate-adjusted learner with CRPS | Conditional normalizing flows on HC-MNIST · HC-MNIST, lower bound | W2 out: 1.011 -> 0.948 | Helped |
| Use W2² rather than CRPS as the AU-learner target risk (ablation) | AU-CNFs on HC-MNIST · HC-MNIST, upper bound | rCRPSout: 0.347 -> 0.422 | Hurt |
| Use W2² rather than CRPS as the AU-learner target risk (ablation) | AU-CNFs on HC-MNIST · HC-MNIST, upper bound | W2 out: 0.940 -> 1.065 | Hurt |
| Use W2² rather than CRPS as the AU-learner target risk (ablation) | AU-CNFs on HC-MNIST · HC-MNIST, lower bound | rCRPSout: 0.357 -> 0.415 | Hurt |
| Use W2² rather than CRPS as the AU-learner target risk (ablation) | AU-CNFs on HC-MNIST · HC-MNIST, lower bound | W2 out: 0.948 -> 1.025 | Hurt |
Surprising findings
- Plug-in and CA-learners can match or beat the AU-learner in low-sample settings and under severe overlap violations (IHDP100).
Limitations
- Makarov bounds are only pointwise sharp, not uniformly sharp; the bounds are not the joint solution.
- Assumes finite argmax/argmin sets (pathwise differentiability); non-regular case not covered.
- Scaling gamma can violate CDF monotonicity/[0,1] constraints; fixed gamma values chosen empirically.
Experimental setup
Datasets: synthetic data (dx=2, normal/multi-modal/exponential outcomes) HC-MNIST IHDP100 COVID-19 lockdown observational dataset
Benchmarks: synthetic benchmarks HC-MNIST IHDP100
Metrics: rCRPS Wasserstein-2 distance
Baselines: Plug-in CNF IPTW-CNF CA-CNFs (CRPS) CA-CNFs (W2^2) Plug-in DKME
Builds on: Makarov bounds DR-learner CA-learner plug-in estimator interventional normalizing flows
Closest papers by meaning
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- A Non-parametric Direct Learning Approach to Heterogeneous Treatment Effect Estimation under Unmeasured Confounding (NeurIPS 2024 · similarity 0.87)
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