Statistical Fidelity

Measures how closely the marginal distributions of individual columns in the synthetic data match the real data.

• Kolmogorov-Smirnov Test: Quantifies the maximum distance between cumulative distribution functions.
• Jensen-Shannon Divergence: A symmetric, smoothed measure of distance between probability distributions.
• Histogram Intersection: Evaluates overlap in binned frequency counts.

High univariate fidelity ensures that basic statistical aggregates—means, medians, and quantiles—are preserved for every attribute independently.

Evaluates whether the pairwise relationships between columns are maintained in the synthetic output.

• Pearson Correlation Matrix: Compares linear correlation coefficients between all numerical column pairs.
• Cramér's V: Measures association strength between categorical variables.
• Correlation Distance: The Frobenius norm of the difference between real and synthetic correlation matrices.

Preserving bivariate structure is critical for downstream models that rely on feature interactions, such as linear regression or logistic classifiers.

The most stringent test of fidelity: whether the synthetic data captures the full joint probability distribution across all dimensions simultaneously.

• Propensity Score Matching (PSM): Trains a classifier to distinguish real from synthetic records; a score near 0.5 indicates indistinguishability.
• Wasserstein Distance: Measures the minimum energy required to morph the synthetic distribution into the real one in high-dimensional space.
• Density Ratio Estimation: Quantifies local discrepancies in the joint density function.

High multivariate fidelity ensures that complex, non-linear interactions and rare edge cases are faithfully reproduced.

Validates that foreign key relationships between generated tables are logically consistent and complete.

• Orphan Record Rate: The percentage of synthetic child records referencing non-existent parent keys—must be zero.
• Join Cardinality Preservation: Ensures one-to-many and many-to-many relationships maintain their real-world multiplicity ratios.
• Cascade Integrity: Verifies that relational dependencies across three or more tables remain coherent.

This dimension is essential for synthesizing entire relational databases rather than isolated flat files.

For time-series or event-sequence data, fidelity requires that chronological dependencies and state transitions are preserved.

• Autocorrelation Function (ACF): Compares lagged correlation structures between real and synthetic sequences.
• Markov Transition Matrix: Validates that the probability of moving from one state to another is accurately reproduced.
• Event Gap Distribution: Ensures the distribution of inter-arrival times between sequential events is maintained.

Without temporal coherence, synthetic transaction logs or sensor streams become useless for forecasting and anomaly detection models.

Statistical fidelity exists in tension with formal privacy guarantees. The privacy-utility trade-off must be explicitly managed.

• Epsilon vs. Fidelity Curve: As differential privacy noise increases (lower epsilon), distributional similarity degrades predictably.
• Attribute Disclosure Risk: Measures the adversary's ability to infer sensitive attributes from non-sensitive synthetic columns.
• Singling-Out Robustness: Validates that no synthetic record uniquely maps to a single real individual.

The goal is to operate at the optimal point on the Pareto frontier where maximum utility is achieved for a given privacy budget.