When evaluating synthetic data, we often talk about two main goals: achieving high fidelity and ensuring high utility. While these terms might sound similar, they represent distinct aspects of data quality, and understanding the difference is significant for assessing whether your generated data is truly useful.

Fidelity: How Similar is it to the Real Thing?

Fidelity refers to how closely the statistical properties of the synthetic dataset match those of the original, real dataset. Think of it as the likeness or resemblance. High-fidelity synthetic data mirrors the real data in terms of:

Basic Statistics: Features in the synthetic data should have similar means ( $\mu$ ), standard deviations ( $\sigma$ ), medians, and ranges as the corresponding features in the real data.
Distributions: The overall shape of the data distribution for each feature should look similar. If a feature in your real data follows a normal distribution, the synthetic version should ideally follow a similar normal distribution. Tools like histograms and density plots, which we discussed earlier, are primary ways to check this.
Correlations: The relationships between different features should be preserved. If two variables are strongly positively correlated in the real data, they should exhibit a similar correlation in the synthetic data.

Essentially, fidelity focuses on recreating the patterns and structure observed in the source data. We use the statistical comparisons and visual inspection methods covered previously to measure fidelity. The closer the synthetic data's characteristics are to the real data's characteristics, the higher its fidelity.

Utility: How Well Does it Work for the Job?

Utility, on the other hand, refers to how effective the synthetic data is for a specific downstream task, usually training a machine learning model. It measures the usefulness of the data for its intended purpose. High utility means that a model trained only on the synthetic data performs well when evaluated on real data.

Measuring utility typically involves a practical test:

Train on Synthetic: Train your machine learning model using only the generated synthetic data.
Test on Real: Evaluate the performance of this model on a held-out set of real data.

If the model performs well on the real test set (e.g., achieves high accuracy, low error, or other relevant performance metrics), the synthetic data is considered to have high utility for that specific task. Utility is task-dependent; data with high utility for a classification task might not have high utility for a regression task, even if derived from the same real dataset.

The Relationship: Fidelity vs. Utility

You might assume that high fidelity automatically leads to high utility. Often, there's a strong positive correlation. If synthetic data accurately captures the underlying patterns of the real data (high fidelity), a model trained on it is likely to generalize well to real data (high utility).

However, this isn't always the case:

High Fidelity, Low Utility: It's possible to generate data that perfectly matches the statistical summaries of the real data but fails to capture subtle, complex relationships needed for the specific ML task. The synthetic data might look right on the surface (matching means, variances) but miss intricate patterns the model needs to learn.
Lower Fidelity, High Utility: Sometimes, synthetic data that slightly deviates from the real data's exact distributions can actually improve model performance. For example, intentionally oversampling rare but important cases (like fraudulent transactions or rare disease diagnoses) might reduce overall statistical fidelity but significantly boost the model's utility for detecting those specific cases. Similarly, certain data augmentation techniques on images might slightly lower strict fidelity but improve model robustness, leading to higher utility.

The choice between prioritizing fidelity or utility often depends on the project's goals:

If the main goal is privacy preservation or creating a realistic data replica for sharing, high fidelity might be the primary objective.
If the main goal is to improve model performance, especially in scenarios with limited real data or class imbalance, utility takes center stage, even if it means sacrificing perfect statistical resemblance.

This diagram illustrates the two primary goals in evaluating synthetic data. Fidelity focuses on similarity to real data properties, while Utility focuses on performance for a specific machine learning task. Evaluation metrics assess both aspects, which are often related but distinct.

In practice, a good evaluation strategy considers both. You often start by aiming for reasonable fidelity using statistical checks and visualizations. Then, you confirm its value by measuring its utility for your target machine learning application. Understanding this distinction helps you choose the right evaluation methods and interpret the results effectively, ensuring your synthetic data truly serves its purpose.