Research map / Probabilistic and scientific modeling / Treatment effects
Exploiting Geometry for Treatment Effect Estimation via Optimal Transport
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Proposes OTCI, a semi-relaxed fused Gromov-Wasserstein optimal transport model with entropic marginal regularization that learns control-sample weights for ATT estimation, solved with projected mirror descent.
Problem
Estimating average treatment effect on the treated from observational data under confounding bias caused by imbalanced confounder distributions; existing re-weighting relies on propensity models or low-order moment alignment that is sensitive to outliers.
Approach
Connects ATT estimation error to the Kantorovich optimal transport problem and learns control weights by combining inter-group Wasserstein cost with intra-group Gromov-Wasserstein metric consistency, plus a negative entropic regularizer on the marginal, optimized by projected mirror descent with KL geometry.
Key results
- On LaLonde, OTCI achieves MAE 192.364 vs. 289.689 for OTW and 382.277 for causalOT (best among compared methods).
- On Twins, OTCI achieves MAE 0.003 vs. 0.005-0.009 for baselines.
- On the toy outlier example, OTCI (both geometries) obtains MAE 0.347 vs. 0.473 for Ebal(1) and 0.517 for Ebal(2), and assigns near-zero weight to outliers.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use OTCI instead of OTW | ATT estimation · LaLonde | MAE: 289.689±198.828 -> 192.364±120.783 | Helped |
| Use OTCI instead of ARB | ATT estimation · Twins | MAE: .005±.004 -> .003±.002 | Helped |
| Add inter-group geometry to moment-based Ebal(1) | OTCI on the toy example · Toy example | MAE: .473 -> .407 | Helped |
| Add intra-group geometry to moment-based Ebal(1) | OTCI on the toy example · Toy example | MAE: .473 -> .355 | Helped |
| Add inter-group geometry to the method using only intra-group geometry (ablation) | OTCI on the toy example · Toy example | MAE: .355 -> .347 | Helped |
| Add intra-group geometry to the method using only inter-group geometry (ablation) | OTCI on the toy example · Toy example | MAE: .407 -> .347 | Helped |
| Use only inter-group geometry instead of both inter- and intra-group geometry (ablation) | OTCI · Toy example | MAE: .347 -> .407 | Hurt |
| Use only intra-group geometry instead of both inter- and intra-group geometry (ablation) | OTCI · Toy example | MAE: .347 -> .355 | Hurt |
Surprising findings
- Using only inter-group or only intra-group geometry is insufficient; the combination is needed for best results in the toy outlier study.
Limitations
- Relies on the strong ignorability assumption and on the Kantorovich bound being tight, which requires conditions on the outcome functions.
- Sensitivity analysis shows performance depends on trade-off parameters alpha and gamma_c, with stable range only in a limited region.
- Evaluation limited to two real datasets and simulations; no runtime or scalability analysis reported.
Experimental setup
Datasets: LaLonde (NSW/CPS) Twins synthetic Gaussian and non-Gaussian simulations 2D toy example with outliers
Benchmarks: LaLonde Twins simulation data (Gaussian, non-Gaussian) toy example with outliers
Metrics: MAE of ATT
Baselines: IPW DR CBPS ARB Ebal DCB BART CFR OTW causalOT
Builds on: Kantorovich optimal transport fused Gromov-Wasserstein entropy balancing differentiated confounder balancing causal optimal transport
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