CTGAN

CTGAN addresses the failure of min-max normalization on complex continuous columns by introducing a variational Gaussian mixture model (VGM). Each continuous column is modeled as a weighted sum of multiple Gaussian modes, and each value is represented by a one-hot vector indicating its sampled mode and a scalar value representing its normalized position within that mode. This allows the generator to learn and reproduce multimodal, non-Gaussian distributions such as bimodal patient age distributions or highly skewed lab values.

To prevent the generator from ignoring minority classes in highly imbalanced categorical columns (e.g., rare disease codes), CTGAN employs a training-by-sampling strategy. During training, the conditional vector and real data are sampled according to the log-frequency of each category rather than the raw data distribution. This forces the model to learn a balanced representation of all categories, ensuring that synthetic data faithfully represents rare but critical clinical events.

CTGAN is a conditional GAN that injects a condition vector directly into both the generator and discriminator. This vector specifies which discrete category the generator should produce, enabling controlled generation of specific data slices. The discriminator evaluates not only the realism of the row but also its consistency with the specified condition, enforcing semantic integrity between conditional attributes and generated values.

The generator uses a deep fully connected neural network with batch normalization and ReLU activations to transform a concatenated latent vector and condition vector into a synthetic row. The discriminator mirrors this with a fully connected architecture using leaky ReLU and dropout layers. This design is intentionally straightforward, relying on the mode-specific normalization and conditional training to handle complexity rather than architectural gimmicks.

CTGAN adopts the Wasserstein GAN with Gradient Penalty (WGAN-GP) loss function to mitigate mode collapse and training instability common in original GAN formulations. The gradient penalty enforces the 1-Lipschitz constraint on the discriminator by penalizing gradients that deviate from a norm of 1, providing a more meaningful convergence metric and enabling more reliable training across diverse tabular datasets.

While CTGAN does not provide formal differential privacy guarantees out of the box, its generative process inherently disrupts one-to-one mapping between real and synthetic records. The stochastic latent space sampling and mode-specific normalization ensure that generated rows are novel combinations of learned patterns, not memorized copies. For regulated healthcare use cases, CTGAN can be combined with differentially private stochastic gradient descent (DP-SGD) to add formal privacy bounds.

A core innovation within CTGAN that addresses the challenge of non-Gaussian, multimodal continuous distributions. Rather than applying a single min-max or Z-score normalization, CTGAN fits a variational Gaussian mixture model (VGM) to each continuous column. This decomposes complex distributions into multiple Gaussian components, each with its own mean and standard deviation. During generation, the model selects a mode and samples from the corresponding normalized distribution, enabling accurate representation of columns with multiple peaks or heavy tails—common in healthcare cost data and laboratory values.

A conditional sampling strategy designed to combat class imbalance in discrete columns. Standard GAN training randomly samples real data, causing the generator to ignore rare categories. CTGAN's training-by-sampling instead:

• Uniformly selects a discrete column
• Uniformly selects a category from that column
• Samples a real row matching that category This forces the discriminator to evaluate every category equally often, compelling the generator to learn high-quality representations of even severely underrepresented classes—critical for generating synthetic records of rare diseases or adverse drug events.

A mathematical framework providing provable privacy guarantees that CTGAN can optionally incorporate. By injecting calibrated noise into the training gradients—typically via the DP-SGD optimizer—the resulting synthetic data carries a formal epsilon guarantee that bounds the influence of any single training record. This transforms CTGAN from a heuristic privacy tool into a mathematically rigorous solution suitable for sharing synthetic clinical data under regulations like HIPAA. The trade-off is a controlled degradation in statistical fidelity as the privacy budget decreases.

The gold-standard evaluation paradigm for CTGAN output. TSTR measures synthetic data utility by:

1. Training a downstream machine learning model exclusively on synthetic data
2. Evaluating that model on a held-out real test set
3. Comparing performance against a model trained on real data If the TSTR score approaches the real-data baseline, the synthetic data captures the predictive relationships present in the original dataset. This is more rigorous than statistical similarity metrics alone, as it validates that the generated data preserves the feature-target mappings essential for clinical prediction models.