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A Generative Approach for Treatment Effect Estimation under Collider Bias: From an Out-of-Distribution Perspective
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Reframes collider bias in treatment effect estimation as an OOD problem and proposes C2GAM, a coupled pair of generators and discriminators that generates missing unselected samples to combine with observational data before fitting any CATE estimator.
Problem
Estimating conditional average treatment effects from observational data affected by collider bias (non-random selection jointly determined by treatment and outcome), where the observational distribution differs from the target population and only a small representative sample is unbiased.
Approach
Treat the selection indicator S as an environment label (S=1 seen, S=0 unseen) and use a GAN-based coupled framework: one generator creates missing S=0 samples, another generates S labels for the small representative data, with two discriminators aligning distributions and a Wasserstein-based stopping criterion; generated samples are then combined with observational data to train standard CATE est
Key results
- On synthetic data with n_rep=500, C2GAM+CFR reaches sqrt(PEHE) 0.984 on S=1 and 1.083 on S=0, versus 2.035 and 2.923 for CFR on observational data alone.
- C2GAM+BNN achieves 0.977 (S=1) and 1.201 (S=0) on synthetic data, improving over the best baseline CW at 1.867 and 2.581.
- On real-world datasets, C2GAM+DRCFR gives 1.064 on IHDP S=1 and 0.296 on Twins S=1, the best results among compared methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use C2GAM-generated samples with CFR instead of the CW data-fusion baseline | CFR · Synthetic, S = 1 samples | √PEHE: 1.867±0.067 -> 0.984±0.074 | Helped |
| Use C2GAM-generated samples with CFR instead of the CW data-fusion baseline | CFR · Synthetic, S = 0 samples | √PEHE: 2.581±0.109 -> 1.083±0.086 | Helped |
| Use C2GAM-generated samples with DRCFR instead of the strongest listed baseline | DRCFR · IHDP, S = 1 samples | √PEHE: 1.391±0.288 -> 1.064±0.120 | Helped |
| Use C2GAM-generated samples with DRCFR instead of the CW data-fusion baseline | DRCFR · IHDP, S = 0 samples | √PEHE: 1.496±0.115 -> 0.979±0.282 | Helped |
| Use C2GAM-generated samples with DRCFR instead of GANITE | DRCFR · Twins, S = 1 samples | √PEHE: 0.329±0.022 -> 0.296±0.021 | Helped |
| Use C2GAM-generated samples with DRCFR instead of the CW data-fusion baseline | DRCFR · Twins, S = 0 samples | √PEHE: 0.381±0.069 -> 0.301±0.030 | Helped |
| Use C2GAM-generated samples with DRCFR instead of the CW data-fusion baseline | DRCFR · ACIC, S = 1 samples | √PEHE: 1.958±0.155 -> 1.675±0.299 | Helped |
| Use C2GAM-generated samples with DRCFR instead of the CW data-fusion baseline | DRCFR · ACIC, S = 0 samples | √PEHE: 2.376±0.175 -> 1.876±0.410 | Helped |
| Add the selection indicator generator Gs (ablation) | C2GAM with CFR · Synthetic, S = 1 samples | √PEHE: 1.453±0.649 -> 0.984±0.074 | Helped |
| Add the unselected samples generator Gd (ablation) | C2GAM with CFR · Synthetic, S = 1 samples | √PEHE: 1.649±0.369 -> 0.984±0.074 | Helped |
| Add the selected data discriminator Do (ablation) | C2GAM with CFR · Synthetic, S = 1 samples | √PEHE: 1.205±0.434 -> 0.984±0.074 | Helped |
| Add the unselected data discriminator Du (ablation) | C2GAM with CFR · Synthetic, S = 1 samples | √PEHE: 1.595±0.410 -> 0.984±0.074 | Helped |
Surprising findings
- Using only the small representative data often outperforms combining it with the biased observational data, which the authors attribute to the small size of the representative set and the non-target-population combination.
- Training on observational data alone performs worst for CATE estimation even though it can fit factual outcomes well.
Limitations
- C2GAM relies on training generative models, which can be hard for complex, high-dimensional data with limited samples.
- Evaluated only on relatively small, semi-synthetic benchmarks with manually introduced collider bias.
- Requires a small representative dataset without collider bias to be available.
Experimental setup
Datasets: IHDP Twins ACIC 2016 synthetic collider-biased data
Benchmarks: IHDP Twins ACIC 2016 synthetic collider-biased data
Metrics: PEHE (sqrt)
Baselines: Doubly Robust Causal Forest CEVAE GANITE TEDVAE BNN TARNet CFR DRCFR ES-CFR IPSW AIPSW
Builds on: GAN BNN CFR DRCFR IPSW
Closest papers by meaning
- Learning Shadow Variable Representation for Treatment Effect Estimation under Collider Bias (ICML 2024 · similarity 0.90)
- Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing (AAAI 2024 · similarity 0.86)
- Enhancing Treatment Effect Estimation via Active Learning: A Counterfactual Covering Perspective (ICML 2025 · similarity 0.85)
- Adversarially Balanced Representation for Continuous Treatment Effect Estimation (AAAI 2024 · similarity 0.85)
- Coupling Generative Modeling and an Autoencoder with the Causal Bridge (NeurIPS 2025 · similarity 0.85)
- Doubly robust identification of treatment effects from multiple environments (ICLR 2025 · similarity 0.84)
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