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Unified Covariate Adjustment for Causal Inference
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Introduces unified covariate adjustment (UCA), a class of sum-product causal estimands covering SBD, front-door, Tian's adjustment and counterfactual directed effects, and a scalable doubly robust DML-based estimator (DML-UCA) with finite-sample guarantees.
Problem
Existing doubly robust estimators for causal effects cover only sequential back-door adjustment, while estimators for broader identification functionals (front-door, Tian's adjustment, general obsID/gID) are not scalable due to summation over high-dimensional variables.
Approach
Define the UCA class of sum-product functionals in which each conditional factor may come from a different distribution (allowing a variable to be fixed in some factors and summed in others), and build a DML estimator using nested regression nuisances and ratio nuisances with empirical bifurcation, achieving polynomial-time computation.
Key results
- DML-UCA's running time scales polynomially, while FD (Fulcher et al., 2019) and Verma/Jung estimators (Jung et al., 2021a) grow rapidly with the dimension of summed variables until timeout at 300 seconds.
- In AAE plots across sample sizes n = 2500 to 20000, DML-UCA outperforms the existing FD, Verma and Jung estimators in all three simulated examples with fast convergence.
- Theoretical finite-sample guarantee and asymptotic analysis show DML-UCA converges at rate n^-1/2 when nuisances converge at n^-1/4, with doubly robust error decomposition.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DML-UCA instead of the existing estimator | Front-door adjustment · Front-door adjustment | running time | Helped |
| Use DML-UCA instead of the existing estimator | Verma's equation · Verma's equation | running time | Helped |
| Use DML-UCA instead of the existing estimator | Jung's equation · Jung's equation | running time | Helped |
| Use DML-UCA instead of the existing estimator | Front-door adjustment · Front-door adjustment | AAE | Helped |
| Use DML-UCA instead of the existing estimator | Verma's equation · Verma's equation | AAE | Helped |
| Use DML-UCA instead of the existing estimator | Jung's equation · Jung's equation | AAE | Helped |
Surprising findings
- The napkin estimand (quotient of sum-products) is not expressible in the UCA class, showing a limit of the framework.
Limitations
- Not all functionals are UCA-expressible, e.g., the napkin estimand and general obsID/gID cases are outside the class.
- Simulations use nuisance estimates from XGBoost and enforced noise on nuisances; only simulated data are evaluated.
- Scalable estimators for general obsID/gID estimands beyond UCA remain undeveloped.
Experimental setup
Datasets: simulated data from SCMs for front-door, Verma, and Jung et al. (2021a) graphs
Benchmarks: simulated SCM data (FD, Verma's equation, Jung's equation)
Metrics: running time average absolute error (AAE)
Baselines: Fulcher et al. (2019) FD estimator DML-ID (Jung et al., 2021a) Bhattacharya et al. (2022) Tian's adjustment estimator Plug-in IPW OM AIPW
Builds on: DML (Chernozhukov et al., 2018) sequential back-door adjustment Tian's adjustment DML-ID (Jung et al., 2021a) Fulcher et al. (2019) front-door estimator
Closest papers by meaning
- Complete Graphical Criterion for Sequential Covariate Adjustment in Causal Inference (NeurIPS 2024 · similarity 0.91)
- Causal Inference with Conditional Front-Door Adjustment and Identifiable Variational Autoencoder (ICLR 2024 · similarity 0.89)
- Generalized Bayes for Causal Inference (NeurIPS 2026 · similarity 0.88)
- Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants (ICML 2025 · similarity 0.87)
- Structural Causal Bottleneck Models (NeurIPS 2026 · similarity 0.87)
- Doubly robust identification of treatment effects from multiple environments (ICLR 2025 · similarity 0.87)
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