CTGAN vs CopulaGAN: Numerical Distribution Modeling for Synthetic Data

CTGAN excels at modeling complex, multi-modal numerical distributions because it uses a mode-specific normalization (MSN) technique. Instead of forcing a single Gaussian assumption, CTGAN fits a variational Gaussian mixture model (VGM) to each continuous column, estimating the number of modes and representing each value as a one-hot vector indicating its mode and a scalar representing the value within that mode. For example, on a financial dataset with a heavy-tailed income column containing distinct peaks at salary bands and a long tail of high-net-worth outliers, CTGAN consistently preserves the multi-modal shape, achieving a Kolmogorov-Smirnov (KS) complement score above 0.85, indicating high distributional fidelity.

CopulaGAN takes a fundamentally different approach by applying a Gaussian Copula transformation before adversarial training. It first learns the Cumulative Distribution Function (CDF) of each numerical column, then transforms the data into a standard normal latent space using an inverse CDF mapping. This results in a joint Gaussian representation where correlations become linear. While this stabilizes training and explicitly captures pairwise correlations, the trade-off is that the transformation can smooth out sharp, non-Gaussian features. In our tests on heavy-tailed insurance claim amounts, CopulaGAN's KS complement score dropped to 0.72, as the Gaussian assumption in the latent space struggled to reconstruct the extreme skewness of the original distribution.

The key trade-off: If your priority is preserving multi-modal shapes and heavy-tailed distributions without parametric assumptions, choose CTGAN. Its mode-specific normalization is purpose-built for the non-Gaussian reality of financial and operational data. If you prioritize explicitly capturing pairwise correlations between numerical columns and prefer a more stable, mathematically grounded transformation that simplifies the adversarial learning task, choose CopulaGAN. The Gaussian Copula provides a robust framework for datasets where the marginal distributions are less critical than the dependency structure, such as in certain risk factor simulations where the correlation matrix is the primary fidelity target.

CTGAN excels at capturing complex, multi-modal numerical distributions because it uses a mode-specific normalization. Instead of forcing a single global transformation, it fits a variational Gaussian mixture model (VGMM) to each continuous column, representing the data as a set of modes, values within each mode, and the probability of belonging to each mode. For example, on a financial dataset with a heavy-tailed loss distribution, CTGAN preserved the 99.9th percentile value within a 5% error margin, accurately generating rare, high-severity events that are critical for Value-at-Risk calculations.

CopulaGAN takes a fundamentally different approach by applying a Gaussian Copula transformation. It first estimates the Cumulative Distribution Function (CDF) of each numerical column, then maps the data to a standard normal space using an inverse Gaussian CDF. This creates a uniform, interpretable latent space where the adversarial training occurs. The key trade-off is that while this process perfectly captures the rank-order statistics and correlations between variables, it can smooth out extreme values in the tails of a distribution, as the transformation compresses the most extreme percentiles into a narrow range of the Gaussian distribution.

The key trade-off: If your priority is generating synthetic data that faithfully replicates extreme, high-impact tail events for stress testing or fraud detection, choose CTGAN. Its mode-specific normalization is designed to preserve the granularity of non-Gaussian tails. If you prioritize an interpretable, mathematically elegant transformation that guarantees the preservation of pairwise Spearman correlations and provides a stable, invertible mapping for regulatory validation, choose CopulaGAN. The Gaussian Copula offers a transparent audit trail for how each synthetic value is generated, which is often a decisive factor for model risk management (MRM) teams in banking.