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Reducing Balancing Error for Causal Inference via Optimal Transport
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Proposes OICL, an optimal-transport method for ATE estimation that jointly learns sample weights (transport marginals), a projection-based cost function, and outcome-guided cost terms to reduce a defined balancing error.
Problem
Confounding bias in average treatment effect (ATE) estimation from observational data depends on choosing an appropriate distribution-shift metric for balancing treated and control groups; existing moment and IPM metrics are hard to choose or insufficient.
Approach
Defines a generic balancing error on reweighted samples, bounds it by the Wasserstein (Kantorovich dual) discrepancy, and learns both the sample weights as OT marginals and a cost function (linear projection with Stiefel constraint) guided by factual outcomes, optimized with entropic regularization and alternating updates.
Key results
- On IHDP, OICL achieves MAE 0.0698 ± 0.0617, the best among compared methods (next best P-CBIPM-type/DKLITE around 0.087-0.090).
- On LaLonde, OICL achieves MAE 146.3 ± 141.8, outperforming P-CBIPM (148.3) and DR-type baselines (211.1 for DR).
- On simulated Gaussian and non-Gaussian data, OICL attains the lowest MAE in most settings, e.g., 0.0138 ± 0.0177 in the non-Gaussian setting with αc=0.3 (as parsed from Table 1).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use OICL instead of the strongest listed baseline | ATE estimation · Twins (1e-2) | MAE: 0.1725 ± 0.1238 -> 0.1674 ± 0.1733 | Helped |
| Use OICL instead of the strongest listed baseline | ATE estimation · Lalonde | MAE: 148.2635 ± 89.1910 -> 146.3449 ± 141.7637 | Helped |
| Use OICL instead of the strongest listed baseline | ATE estimation · IHDP | MAE: 0.0864 ± 0.0622 -> 0.0698 ± 0.0617 | Helped |
| Vary the factual-outcome guidance strengths λc and λt (ablation) | OICL · Lalonde | MAE | Mixed |
| Vary the entropic regularization strengths γc and γt (ablation) | OICL · Lalonde | MAE | Mixed |
Limitations
- Balancing-error analysis relies on strong ignorability and assumptions for consistency and convergence rates (n^{-1/d}).
- Sensitivity to trade-off hyperparameters (lambda, gamma) shown on LaLonde; performance worsens at extreme values.
Experimental setup
Datasets: LaLonde (NSW + PSID) Twins IHDP synthetic Gaussian and Gaussian-mixture data
Benchmarks: LaLonde Twins IHDP synthetic Gaussian simulation synthetic non-Gaussian simulation
Metrics: mean absolute error of ATE estimate
Baselines: IPW DR CBPS ARB EBAL(1) EBAL(2) CFR OTW P-CBIPM N-CBIPM ℓ1-TCL DKLITE
Builds on: Kantorovich optimal transport inverse propensity weighting entropy-regularized optimal transport (Cuturi 2013) CFR entropy balancing
Closest papers by meaning
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