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Debiasing Synthetic Data Generated by Deep Generative Models
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Proposes a generator-agnostic debiasing post-processing step (mean shifting plus EIC-based estimators) for synthetic data from deep generative models, restoring root-n convergence and near-nominal CI coverage for means and regression coefficients.
Problem
Synthetic data from deep generative models induce bias and slow (sub-root-n) convergence of standard errors in downstream statistical estimates, so p-values and confidence intervals are invalid.
Approach
Adapt debiased/targeted machine learning to synthetic data: shift the DGM-generated samples by the estimated bias (computed from a large DGM sample and the original data) so the bias term from the generator vanishes, and use EIC-based estimators; the resulting variance is approximated by (1/m + 1/n) E[phi^2], generalising the sqrt(1+m/n) correction. No retraining of the DGM is needed.
Key results
- Debiased synthetic data achieves near-nominal 95% CI coverage for the population mean of age across all sample sizes and both DGMs, whereas default synthetic data coverage decreases with n.
- Estimated SE convergence exponent for the mean of age rises from 0.01 (CTGAN) and 0.21 (TVAE) in default synthetic data to 0.50 and 0.47 after debiasing.
- In the IST case study with n=500, default synthetic data falsely rejected the risk difference in 7 of 15 repetitions, while debiased synthetic data avoided this false-positive pattern.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Debias synthetic data for the population mean | CTGAN and TVAE synthetic data · Simulation: mean age | 95% CI coverage | Helped |
| Debias synthetic data for the regression coefficient | TVAE synthetic data · Simulation: therapy effect on blood pressure adjusted for stage | 95% CI coverage | Helped |
| Debias synthetic data for the regression coefficient | CTGAN synthetic data · Simulation: therapy effect on blood pressure adjusted for stage | 95% CI coverage | Helped |
| Debias synthetic data for the population mean (ablation) | CTGAN synthetic data · Simulation: mean age | empirical SE convergence exponent: 0.01 [-0.16; 0.18] -> 0.50 [0.46; 0.54] | Helped |
| Debias synthetic data for the population mean (ablation) | TVAE synthetic data · Simulation: mean age | empirical SE convergence exponent: 0.21 [0.04; 0.39] -> 0.47 [0.44; 0.50] | Helped |
| Debias synthetic data for the regression coefficient (ablation) | CTGAN synthetic data · Simulation: therapy effect on blood pressure adjusted for stage | empirical SE convergence exponent: 0.31 [0.22; 0.40] -> 0.43 [0.31; 0.55] | Helped |
| Debias synthetic data for the regression coefficient (ablation) | TVAE synthetic data · Simulation: therapy effect on blood pressure adjusted for stage | empirical SE convergence exponent: 0.09 [-0.13; 0.31] -> 0.46 [0.38; 0.55] | Helped |
| Debias synthetic data | CTGAN and TVAE · IST risk difference for death, n=m=500 | false-positive conclusions among 15 repetitions: 7 out of these 15 repetitions | Helped |
| Use sample splitting when training the DGM and applying the debiasing step (ablation) | Debiasing strategy · Simulation: therapy effect on blood pressure adjusted for stage | 95% CI coverage | Helped |
Surprising findings
- Debiasing the regression coefficient with CTGAN did not reach nominal coverage, and the MLE-based SE still underestimated the empirical SE despite debiasing.
- Preliminary simulations suggested sample splitting (cross-fitting) did not help, so the main results omit it despite theory requiring it.
Limitations
- Only low-dimensional settings (simulation with four variables and two case studies) were studied, where DGMs may be less suited.
- Coverage was not guaranteed at nominal level for CTGAN regression coefficients, since sample splitting was not used.
- Regression debiasing requires sampling conditionally on covariates, which not all DGMs support; the theory applies only to pathwise differentiable parameters.
Experimental setup
Datasets: simulated hypothetical disease data International Stroke Trial (IST) Adult Census Income
Benchmarks: simulation study International Stroke Trial Adult Census Income
Metrics: empirical coverage of 95% CI bias standard error convergence rate exponent inverse KL divergence
Baselines: default synthetic data (no debiasing) original data analysis CTGAN TVAE
Builds on: debiased machine learning targeted maximum likelihood estimation multiple imputation for synthetic data CTGAN TVAE
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