After computing a battery of metrics across fidelity, utility, and privacy dimensions, the raw numbers can be overwhelming. A table full of scores might contain all the information, but it rarely tells the full story in an accessible way. Effective visualization transforms these numerical results into clear, interpretable insights, making it easier to understand the strengths and weaknesses of a synthetic dataset and communicate these findings to stakeholders. The goal is not just to present data, but to guide interpretation and support informed decisions about whether a synthetic dataset is fit for purpose.

Choosing the Right Visual Representation

The first step is selecting the appropriate chart type for the specific metric or comparison you want to illustrate. Different visualizations excel at highlighting different aspects of the data.

Distributions: Histograms, density plots (Kernel Density Estimates - KDEs), and Quantile-Quantile (Q-Q) plots are standard choices for comparing the distribution of individual features between the real and synthetic datasets. Overlaying synthetic distributions on real ones requires careful use of transparency or distinct color schemes.
Comparisons: Bar charts are effective for comparing single-value metrics (like average performance scores or privacy attack accuracy) across different datasets or models (e.g., real vs. synthetic). Grouped or stacked bar charts can show multiple related metrics simultaneously.
Relationships: Scatter plots are useful for showing the relationship between two continuous variables. Heatmaps are excellent for visualizing matrices, such as correlation matrices or confusion matrices.
Multidimensional Data: Radar charts (spider plots) can provide a compact overview of multiple metrics for one or several datasets, though they become cluttered easily. Dimensionality reduction techniques like PCA or t-SNE followed by scatter plots can help visualize high-dimensional structural similarity, but require careful interpretation as they can distort distances.
Performance Curves: Line charts are standard for plotting performance trade-offs, such as ROC curves (True Positive Rate vs. False Positive Rate) for Membership Inference Attacks or Precision-Recall curves.

Visualizing Statistical Fidelity

Comparing distributions is fundamental to fidelity assessment. While univariate comparisons are straightforward, visualizing multivariate relationships requires more attention.

Univariate Distributions

Side-by-side or overlaid histograms/density plots immediately show differences in shape, center, and spread for individual features.

Overlaid density histograms comparing the distribution of the 'Age' feature in real and synthetic datasets.

Correlation Structure

Heatmaps provide an intuitive way to compare correlation matrices. Place the heatmap for the real data next to the heatmap for the synthetic data, using the same color scale. Differences in patterns immediately highlight where the synthetic data fails to capture dependencies.

Side-by-side heatmaps visualizing the correlation matrices of real and synthetic data. Consistent color scaling allows for direct comparison of dependency structures.

Visualizing Machine Learning Utility

ML utility metrics often involve comparing the performance of models trained on different data sources.

Downstream Task Performance

Bar charts are effective for comparing key performance indicators (KPIs) like accuracy, F1-score, or AUC obtained using different training regimes (TSTR, TRTR, TRTS). Error bars representing confidence intervals or standard deviations across multiple runs add statistical context.

Comparison of AUC scores for two different models across Train-Real/Test-Real (baseline), Train-Synthetic/Test-Real (TSTR utility), and Train-Real/Test-Synthetic (TRTS fidelity) scenarios.

Feature Importance

Comparing feature importance rankings helps assess whether models trained on synthetic data learn similar patterns as those trained on real data. Side-by-side horizontal bar charts can effectively display this comparison.

Side-by-side horizontal bar charts comparing feature importance scores derived from models trained on synthetic versus real data.

Visualizing Privacy Risks

Privacy evaluations often involve metrics derived from attack simulations.

Membership Inference Attacks (MIAs)

The performance of an MIA classifier is typically visualized using an ROC curve or a Precision-Recall curve. The Area Under the Curve (AUC) provides a single summary statistic, often compared against the baseline of 0.5 (random guessing) using a bar chart.

ROC curve illustrating the trade-off between true positive and false positive rates for a Membership Inference Attack classifier. The diagonal dashed line represents random guessing.

Distance-Based Metrics

Metrics like Distance to Closest Record (DCR) can be visualized using histograms or density plots, comparing the distribution of minimum distances for real records versus synthetic records to their nearest neighbors in the training data. Lower distances for synthetic records might indicate potential privacy leakage.

Integrated Views and Dashboards

Often, a single visualization isn't enough. Combining multiple plots into a cohesive report or dashboard provides a holistic view.

Radar Charts

For comparing multiple synthetic datasets or generation methods across several normalized metrics (e.g., a fidelity score, a utility score, a privacy score), radar charts offer a compact visual summary. However, ensure the axes are clearly labelled and avoid plotting too many datasets or metrics, which can make the chart unreadable.

Radar chart comparing two synthetic data generation models (Model A and Model B) across five normalized quality metrics. Larger areas generally indicate better performance on those axes.

Best Practices and Avoiding Misinterpretation

Simplicity and Clarity: Avoid chart junk. Ensure axes are labeled, titles are informative, and legends are clear. Use color purposefully to distinguish categories or highlight findings, drawing from a consistent palette.
Appropriate Scales: Use scales that accurately reflect the data. Avoid truncating axes (especially bar charts starting from non-zero baselines) unless clearly justified and annotated, as this can exaggerate differences. Log scales might be appropriate for data spanning multiple orders of magnitude.
Context is Important: Always present visualizations alongside their numerical metric values and interpretations. Explain what the visualization shows and what conclusions can be drawn.
Dimensionality Reduction Caveats: While PCA and t-SNE plots can be visually appealing for high-dimensional data, remember they are projections. Distances and cluster shapes in the 2D plot may not perfectly reflect the high-dimensional reality. Use them cautiously to gain intuition, not as definitive proof of similarity or difference.
Audience Awareness: Tailor the complexity and type of visualizations to your audience. Stakeholders might prefer high-level summaries (like radar charts or bar charts of key KPIs), while technical teams may need detailed distributional plots or performance curves.

By thoughtfully selecting, designing, and presenting visualizations, you can transform complex evaluation results into compelling evidence that effectively communicates the quality and suitability of your synthetic data.