Benchmarking Different Synthetic Datasets

Often, the goal isn't just to evaluate a single synthetic dataset in isolation, but to compare multiple candidates. Perhaps you've trained several generative models (e.g., a GAN, a VAE, a Diffusion Model) on the same real data, or maybe you've generated datasets using the same model but with different hyperparameter settings. Benchmarking provides a structured way to determine which synthetic dataset, or which generation approach, best meets your requirements for a specific application. Building upon the comprehensive reporting structure discussed earlier, benchmarking introduces a comparative layer to your analysis.

Establishing a Consistent Evaluation Framework

The foundation of effective benchmarking is fairness. To meaningfully compare different synthetic datasets, you must evaluate them under identical conditions. This means:

1. Consistent Metrics: Apply the exact same set of fidelity, utility, and privacy metrics to all candidate datasets.
2. Identical Real Data Splits: Use the same training, testing, and validation splits of the original real data for all evaluations, especially for utility tasks like Train-Synthetic-Test-Real (TSTR).
3. Standardized Downstream Tasks: When assessing utility, use the same machine learning models, hyperparameter settings (or the same tuning process), and evaluation metrics (e.g., Accuracy, F1-score, AUC) across all comparisons.
4. Uniform Privacy Attacks: Employ the same configuration and adversary models when running privacy assessments like Membership Inference Attacks (MIAs).

Any variation in the evaluation setup between datasets can introduce bias, making comparisons unreliable. The automation pipelines discussed previously become particularly valuable here, ensuring consistency and reproducibility across multiple benchmark runs.

Multi-Metric Comparison Techniques

Comparing datasets often involves juggling performance across multiple, potentially conflicting, dimensions (fidelity, utility, privacy). A dataset might excel in statistical fidelity but perform poorly on downstream tasks, while another offers better utility at the cost of slightly higher privacy risks. Visualizations and summary methods are essential for understanding these trade-offs.

Tabular Summaries

The simplest approach is to compile main metrics into a table, with each row representing a synthetic dataset and each column representing an evaluation metric. This provides a direct side-by-side comparison.

Dataset	Kolmogorov-Smirnov (Avg. p-value)	TSTR Accuracy (vs. Real Baseline)	MIA AUC Score	Feature Importance Correlation	Generation Time (min)
GAN (Default HPs)	0.65	92%	0.68	0.75	120
VAE (Latent=32)	0.78	88%	0.59	0.82	45
GAN (Tuned HPs)	0.82	95%	0.65	0.88	180
DP-GAN (Epsilon=1)	0.55	75%	0.52	0.60	210

Visualization for Trade-offs

Visual tools can make complex comparisons more intuitive.

• Radar Charts: These are effective for visualizing performance across several metrics simultaneously. Each axis represents a metric (ideally normalized to a common scale, e.g., 0 to 1), and each polygon represents a dataset. This makes it easy to spot datasets that are strong overall or excel in specific areas.

Radar chart comparing three synthetic datasets across five normalized dimensions: Statistical Fidelity (Kolmogorov-Smirnov test average), TSTR Accuracy relative to baseline, Privacy (inverted MIA score), Feature Importance Correlation, and Generation Efficiency (inversely related to time). Scores are normalized between 0 and 1, where higher is better.

• Pareto Frontiers: In scenarios with clear trade-offs (e.g., Utility vs. Privacy), plotting datasets on a 2D scatter plot can reveal the Pareto frontier. Datasets on this frontier represent optimal choices, meaning you cannot improve one metric without worsening the other. Datasets not on the frontier are "dominated" by at least one dataset on the frontier.

Ranking and Selection Strategies

Once the metrics are gathered and visualized, you need a strategy to select the "best" dataset for your purpose.

Weighted Scoring

If you can quantify the relative importance of different evaluation dimensions for your specific application, you can compute a weighted composite score for each dataset.

1. Normalize Metrics: Scale all metrics to a common range (e.g., 0 to 1), ensuring higher values consistently indicate better performance. For metrics where lower is better (like MIA AUC or generation time), use an inverse scaling (e.g., $1 - \text{normalized\_value}$).
2. Assign Weights: Define weights ($w_i$) for each metric based on application priorities, such that $\sum w_i = 1$. For instance, a high-privacy application might assign a large weight to the privacy metric, while a pure performance task might heavily weight TSTR utility.
3. Calculate Score: Compute the overall score for each dataset $D$ as $Score(D) = \sum_{i} w_i \times \text{NormalizedMetric}_i(D)$.

The dataset with the highest score is considered the best according to your defined priorities. Be aware that this method is sensitive to the chosen weights, which can be subjective. It's often useful to perform sensitivity analysis by varying the weights slightly.

Dominance Analysis

A dataset $A$ dominates dataset $B$ if $A$ performs at least as well as $B$ on all metrics and strictly better on at least one metric. Identifying dominated datasets helps eliminate clearly inferior options without needing explicit weights. The non-dominated datasets form the Pareto set mentioned earlier.

Tiering

Instead of a single top choice, you might categorize datasets into performance tiers (e.g., "Excellent", "Good", "Acceptable", "Unsuitable") based on predefined thresholds for important metrics. This is useful when multiple datasets meet a minimum quality bar, allowing flexibility in selection based on secondary criteria like generation cost.

Considering Generation Cost and Complexity

Benchmarking shouldn't solely focus on quality metrics. Practical considerations are also significant:

• Generation Time: How long does it take to generate the synthetic data? A model producing slightly lower-quality data much faster might be preferable in time-sensitive applications.
• Computational Resources: What are the hardware requirements (GPU, RAM) for training the generator and synthesizing data?
• Ease of Use: How complex is the model to train, tune, and deploy?

These factors should be included in your comparison, perhaps as additional columns in your summary table or as constraints in your selection process.

By systematically benchmarking different synthetic datasets using a consistent framework and appropriate comparison techniques, you can make informed decisions about which generative models, parameters, or specific datasets best serve your needs, balancing the complex relationship of fidelity, utility, privacy, and practical constraints.