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Reducing Confounding Bias without Data Splitting for Causal Inference via Optimal Transport
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Proposes ORIC, a balanced-representation method for binary and continuous treatment effect estimation that models treatment-conditional distributions over all training samples via entropic optimal transport (Sinkhorn), avoiding data splitting.
Problem
Confounding bias in observational causal effect estimation; existing distribution-alignment methods split samples by treatment group, shrinking the sample size available for distribution estimation and alignment.
Approach
Represent every treatment-conditional distribution as a reweighting (via generalized propensity scores) of the full training set and align marginal and conditional distributions with a Sinkhorn Wasserstein distance in representation space, jointly with outcome prediction loss; theory bounds the outcome error gap by Wasserstein distance.
Key results
- On the continuous-treatment synthetic benchmark (beta=0.25), ORIC achieves sqrt(AMSE) 0.1098 vs 0.1155 for the next best VCNet+TR.
- On IHDP binary treatment, ORIC reports sqrt(PEHE) 1.1129, lower than CFRNet's 1.2809 and the other baselines.
- ORIC's running time is 135 s in the continuous setting versus 8-47 s for baselines, described as moderate efficiency.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ORIC instead of VCNet+TR | Continuous-treatment outcome estimation · Synthetic β = 0.25 | √AMSE: 0.1155 ± 0.0305 -> 0.1098 ± 0.0273 | Helped |
| Use ORIC instead of VCNet+TR | Continuous-treatment outcome estimation · Synthetic β = 0.5 | √AMSE: 0.1361 ± 0.0439 -> 0.1234 ± 0.0388 | Helped |
| Use ORIC instead of VCNet+TR | Continuous-treatment outcome estimation · Synthetic β = 0.75 | √AMSE: 0.1442 ± 0.0512 -> 0.1313 ± 0.0464 | Helped |
| Use ORIC instead of VCNet+TR | Continuous-treatment outcome estimation · Synthetic β = 1 | √AMSE: 0.1257 ± 0.0381 -> 0.1168 ± 0.0316 | Helped |
| Use ORIC instead of VCNet+TR | Continuous-treatment outcome estimation · IHDP | √AMSE: 0.3712 ± 0.0465 -> 0.3595 ± 0.0304 | Helped |
| Use ORIC instead of VCNet+TR | Continuous-treatment outcome estimation · News | √AMSE: 0.1675 ± 0.0566 -> 0.1507 ± 0.0406 | Helped |
| Use ORIC instead of the best listed baseline | Binary-treatment outcome estimation · IHDP | √PEHE: 1.2443 ± 2.1300 -> 1.1129 ± 1.4290 | Helped |
| Use ORIC instead of CFRNet | Binary-treatment outcome estimation · IHDP | MAE: 0.1582 ± 0.1986 -> 0.2134 ± 0.3488 | Hurt |
| Use ORIC instead of CFRNet | Binary-treatment outcome estimation · IHDP | √AMSE: 1.2739 ± 1.7038 -> 1.1976 ± 1.3822 | Helped |
| Use ORIC instead of the best listed baseline | Binary-treatment outcome estimation · News | √PEHE: 1.7916 ± 0.5652 -> 1.7183 ± 0.5488 | Helped |
| Use ORIC instead of DKLite | Binary-treatment outcome estimation · News | MAE: 0.2328 ± 0.1272 -> 0.1624 ± 0.1587 | Helped |
| Use ORIC instead of CFRNet | Binary-treatment outcome estimation · News | √AMSE: 2.4187 ± 0.6538 -> 2.3972 ± 0.5678 | Helped |
Surprising findings
- On the News binary benchmark, ORIC's sqrt(PEHE) (1.7183) is not the best; DKLite (1.8172 PEHE) and CFRNet (2.0527) are close, and the sqrt(AMSE) of ORIC (2.3972) trails CFRNet's 2.4187 only slightly, suggesting the method is not uniformly dominant.
Limitations
- Assumes no unobserved confounders (ignorability); unobserved confounding is left to future work.
- Computational cost grows quadratically with sample size and requires discretizing continuous treatments into sampled values.
- Running time is higher than most baselines (135 s vs 8-47 s on continuous setting).
Experimental setup
Datasets: Synthetic (simulated continuous treatment) IHDP News
Benchmarks: Synthetic IHDP News
Metrics: sqrt(AMSE) ADRF curve sqrt(PEHE) MAE running time
Baselines: KNN BART GPS MLP MLP+GPS DRNet ADMIT ACFR VCNet VCNet+TR OLS CFRNet
Builds on: CFRNet (Shalit et al., 2017) ADMIT (Wang et al., 2022) VCNet (Nie et al., 2021) Sinkhorn algorithm (Cuturi, 2013) CausalOT (Li et al., 2021)
Closest papers by meaning
- Reducing Balancing Error for Causal Inference via Optimal Transport (ICML 2024 · similarity 0.91)
- Exploiting Geometry for Treatment Effect Estimation via Optimal Transport (AAAI 2024 · similarity 0.89)
- DiffPO: A causal diffusion model for learning distributions of potential outcomes (NeurIPS 2024 · similarity 0.87)
- Doubly robust identification of treatment effects from multiple environments (ICLR 2025 · similarity 0.86)
- Tightening Causal Bounds via Covariate-Aware Optimal Transport (ICML 2025 · similarity 0.86)
- Marginal Causal Flows for Validation and Inference (NeurIPS 2024 · similarity 0.86)
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