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An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation
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Shows that outcome-invariant data augmentation acts as a soft intervention on the treatment mechanism, introduces IV-like (IVL) regression, and casts DA parameters as IV-like variables to reduce confounding bias in causal effect estimation.
Problem
Causal effect estimation from observational data with unobserved confounders is hard when instrumental variables are unavailable, as is common in computer vision and NLP.
Approach
Outcome-invariant data augmentation is equivalent to a soft intervention on the treatment mechanism, and DA parameters act as IV-like variables; regularizing IV regression with an ERM penalty (IVL regression) and composing it with DA yields a worst-case DA application that reduces confounding bias.
Key results
- On the optical device dataset, DA+ERM reduces nCER from 0.823 (ERM) to 0.513 for the all-augmentations setting, and DA+IVL(CV) reaches 0.533, with both significantly better than ERM.
- In linear simulations, DA+IVL achieves lower causal excess risk than ERM and DA+ERM as confounding increases, while DA+IV regression is unstable.
- On Colored MNIST, DA+IVL(CV) achieves the best overall performance among compared methods, while ERM underperforms.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply outcome-invariant data augmentation with ERM | Optical device estimation · Optical device datasets | nCER: 0.827 ± 0.079 -> 0.617 ± 0.085; 0.827 ± 0.079 -> 0.513 ± 0.082; 0.827 ± 0.079 -> 0.707 ± 0.090; 0.823 ± 0.083 -> 0.513 ± | Helped |
| Add IVL regression to data augmentation, with α selected by CV | DA+ERM · Optical device datasets | nCER: 0.617 ± 0.085 -> 0.623 ± 0.087; 0.513 ± 0.082 -> 0.540 ± 0.085; 0.707 ± 0.090 -> 0.641 ± 0.092; 0.513 ± 0.075 -> 0.533 ± | Mixed |
| Add IVL regression to data augmentation, with α selected by LCV | DA+ERM · Optical device datasets | nCER: 0.617 ± 0.085 -> 0.619 ± 0.087; 0.513 ± 0.082 -> 0.534 ± 0.082; 0.707 ± 0.090 -> 0.662 ± 0.091; 0.513 ± 0.075 -> 0.574 ± | Mixed |
| Apply data augmentation alone | ERM · Linear simulation across varying confounding κ | nCER | Helped |
| Add IVL regression to data augmentation | DA+ERM · Linear simulation across varying confounding κ | nCER | Helped |
| Use DA+IV regression instead of DA+IVL | DA+IVL · Linear simulation across varying confounding κ | nCER | Hurt |
| Vary α; use an intermediate regularization value rather than an arbitrarily small α (ablation) | DA+IVL · Linear simulation, κ = γ = 1 | nCER | Helped |
| Select α using CV or CC (ablation) | DA+IVL · Linear simulation, κ = γ = 1 | nCER | Helped |
| Increase DA strength γ (ablation) | DA+IVL · Linear simulation with κ = 1 | nCER | Helped |
| Use DA strength γ that is too small or too large (ablation) | DA+IVL · Linear simulation with κ = 1 | nCER | No clear effect |
| Apply DA+ERM | ERM · Colored MNIST | test accuracy | Helped |
| Add IVL regression to DA+ERM and select α by CV | Colored MNIST · Colored MNIST | test accuracy | Helped |
Surprising findings
- Arbitrarily small IVL regularization alpha is beneficial in the population theory but suboptimal in finite samples, which the authors attribute to outcome invariance not holding exactly in practice.
- On the optical device dataset, DA+ERM alone achieves the lowest nCER in several settings, with DA+IVL only performing comparably.
Limitations
- Outcome invariance alone does not guarantee reduced confounding bias; domain knowledge is needed to pick DA that targets spurious features.
- Choice of regularization parameter alpha is hard to select in finite samples and relies on in-distribution cross-validation.
- Causal identification from observational data depends on untestable assumptions such as un-confoundedness and exclusion.
Experimental setup
Datasets: optical device dataset Colored MNIST synthetic linear SEM simulations
Benchmarks: Colored MNIST optical device dataset linear SEM simulations
Metrics: normalized causal excess risk (nCER) causal excess risk
Baselines: ERM DA+ERM DA+IV DRO IRM ICP RICE V-REx MM-REx Kania and Wit causal regularization Janzing l1/l2 regularization
Builds on: instrumental variable regression two-stage least squares invariant risk minimization invariant causal prediction
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