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Enhancing Treatment Effect Estimation via Active Learning: A Counterfactual Covering Perspective
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Proposes a counterfactual covering-radius bound for active-learning treatment effect estimation and two model-independent acquisition methods (greedy radius reduction and FCCM coverage maximization) that outperform AL and causal AL baselines on Toy, IBM and CMNIST.
Problem
Data-efficient treatment effect estimation under a limited labeling budget when treatment indicators and covariates are known in the pool but outcomes are costly to label; the PEHE risk is not directly optimizable because counterfactual outcomes are unobserved.
Approach
Derives a probabilistic PEHE upper bound in terms of factual and counterfactual covering radii, then selects samples via a greedy radius-reduction rule and a weighted-graph greedy coverage maximization (FCCM) that counts counterfactual coverage with weight alpha, allowing single-sample acquisition without paired queries.
Key results
- FCCM achieves a sqrt-PEHE gain of about 16-18% over the FCCM- ablation on Toy at 2/5 to 5/5 of budget (e.g., 0.7565 at full budget).
- On CMNIST, FCCM improves over FCCM- by roughly 24-30% across budget stages (1.6790 vs 2.2073 at full budget).
- On IBM the ablation gain is near zero (-1% to 0%) because treated and control distributions overlap heavily.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add counterfactual coverage maximization to FCCM- (ablation) | FCCM · Toy | sqrt PEHE: +0%, +17%, +18%, +18%, +16% | Helped |
| Add counterfactual coverage maximization to FCCM- (ablation) | FCCM · IBM | sqrt PEHE: -1%, -1%, -1%, +0%, +0% | Mixed |
| Add counterfactual coverage maximization to FCCM- (ablation) | FCCM · CMNIST | sqrt PEHE: +24%, +30%, +28%, +25%, +24% | Helped |
| Use FCCM's joint factual and counterfactual coverage acquisition instead of the compared baselines | Treatment effect estimation · Toy, IBM, and CMNIST | sqrt PEHE | Helped |
Surprising findings
- BAIT, a general AL method, outperforms many treatment-effect-specific AL baselines on CMNIST but underperforms on Toy and IBM.
- Current DTEE baselines do not consistently outperform general AL methods across datasets.
Limitations
- FCCM degrades when treatment groups have non-overlapping regions in raw feature space, since no counterfactual pairs exist.
- Theoretical bound relies on Lipschitz continuity and a constant kappa assumption; zero training loss assumption.
- Experiments use simulated and semi-synthetic data only.
Experimental setup
Datasets: Toy (simulated 2D) IBM (Linked Births and Infant Deaths Database semi-synthetic) CMNIST
Benchmarks: Toy IBM CMNIST
Metrics: sqrt PEHE performance gain relative to FCCM-
Baselines: BADGE BAIT LCMD QHTE Causal-BALD MACAL muBALD rhoBALD murhoBALD
Builds on: ProbCover core-set k-Center QHTE MACAL Causal-BALD DUE
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