Research map / Probabilistic and scientific modeling / Treatment effects
Extended Wasserstein-GAN Approach to Causal Distribution Learning: Density-Free Estimation and Minimax Optimality
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Proposes GANICE, a GAN that minimizes an extended Wasserstein distance (diagonal, state-preserving coupling) between generated and target conditional interventional outcome laws, using cell-normalized estimators to avoid density-ratio estimation, with minimax rates for finite and continuous conditioning.
Problem
Estimating full conditional interventional outcome distributions (beyond means) for causal inference, where existing adversarial causal generators lack population risk formulations tied to the identifiable target and often rely on unstable density-ratio estimation.
Approach
Replace factual-coordinate discriminators with a WGAN-style dual under the extended Wasserstein distance, which compares outcome laws only at identical treatment-covariate states; the empirical objective uses cell-normalized observed averages weighted by target masses so overlap density ratios never need estimating.
Key results
- GANICE achieves IHDP extended Wasserstein error 0.286 (SE 0.004), vs. best baseline DiffPO 0.323.
- On TCGA GANICE gets 0.378 (SE 0.005) vs. SCIGAN 0.401; on Jobs 0.209 (SE 0.007) vs. PO-Flow 0.299.
- Theory: minimax rate n^{-a} for finite conditioning and (kappa n)^{-r_aniso} for continuous anisotropic conditioning, up to log factors.
Surprising findings
- Factual-index adversarial imputation objectives identify only treatment-specific conditional marginals, not the joint law of potential outcomes.
Limitations
- Continuous-conditioning guarantees rely on strong regularity assumptions (design regularity, anisotropic W1 smoothness, pointwise latent pushforward).
- Raw single-network implementations need an additional integrated transfer/oscillation condition for the theory.
- Rates characterize approximate population or empirical minimizers, not optimization dynamics.
Experimental setup
Datasets: IHDP TCGA Jobs (NSW + PSID)
Benchmarks: IHDP TCGA Jobs
Metrics: empirical extended Wasserstein error RCT-assisted arm-level Wasserstein error quantile treatment effect error CDF agreement
Baselines: GANITE PO-Flow DiffPO INFs DR-Learner SCIGAN DRNet VCNet
Builds on: WGAN GANITE SCIGAN MCGAN extended Wasserstein distance
Closest papers by meaning
- Conditional Generative Models are Sufficient to Sample from Any Causal Effect Estimand (NeurIPS 2024 · similarity 0.86)
- Modular Learning of Deep Causal Generative Models for High-dimensional Causal Inference (ICML 2024 · similarity 0.85)
- Reducing Balancing Error for Causal Inference via Optimal Transport (ICML 2024 · similarity 0.85)
- Adversarially Balanced Representation for Continuous Treatment Effect Estimation (AAAI 2024 · similarity 0.84)
- DiffPO: A causal diffusion model for learning distributions of potential outcomes (NeurIPS 2024 · similarity 0.84)
- Continuous Treatment Effect Estimation Using Gradient Interpolation and Kernel Smoothing (AAAI 2024 · similarity 0.84)
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