Once you have trained a machine learning model using synthetic data (as in the Train-Synthetic-Test-Real or TSTR framework) and potentially a baseline model using real data, the next step is to rigorously compare their performance. The goal is to quantify how much, if any, performance is lost or gained by using synthetic data for training, compared to using the original real data. This comparison forms the core of the ML utility assessment.

Selecting Appropriate Performance Metrics

The choice of metrics is entirely dependent on the nature of the downstream machine learning task you are evaluating. There is no single universal metric; you must select metrics relevant to the problem you are trying to solve with the model.

Classification Tasks: For problems like predicting categories (e.g., fraud detection, image classification), common metrics include:
- Accuracy: Overall percentage of correct predictions.
- Precision: Proportion of positive identifications that were actually correct. Important when the cost of false positives is high.
- Recall (Sensitivity): Proportion of actual positives that were identified correctly. Important when the cost of false negatives is high.
- F1-Score: The harmonic mean of Precision and Recall, providing a balanced measure.
- Area Under the Receiver Operating Characteristic Curve (AUC-ROC): Measures the model's ability to distinguish between classes across different thresholds.
- Area Under the Precision-Recall Curve (AUC-PR): Often more informative than AUC-ROC for imbalanced datasets.
Regression Tasks: For problems involving predicting continuous values (e.g., predicting house prices, forecasting sales), common metrics include:
- Mean Absolute Error (MAE): Average absolute difference between predicted and actual values.
- Mean Squared Error (MSE): Average squared difference between predicted and actual values. Penalizes larger errors more heavily.
- Root Mean Squared Error (RMSE): The square root of MSE, putting the error back into the original units.
- R-squared ( $R^2$ ): Coefficient of determination, indicating the proportion of variance in the dependent variable predictable from the independent variables.

Choose the metric(s) that best reflect the success criteria for your specific application. Often, evaluating multiple relevant metrics provides a more complete picture of model performance.

The Comparison Process

The standard procedure involves these steps:

Train Baseline Model: Train your chosen machine learning model (e.g., Logistic Regression, Random Forest, Neural Network) using the real training dataset ( $D_{train\_real}$ ).
Train Synthetic Model: Train an identical model architecture, using the same hyperparameters, but this time using the synthetic training dataset ( $D_{train\_synth}$ ). Maintaining identical model configurations is important for a fair comparison.
Evaluate Both Models: Evaluate both the baseline model and the synthetic model on the same held-out real test dataset ( $D_{test\_real}$ ). This is the essence of TSTR – you want to know how well the model trained on synthetic data generalizes to unseen, real-world data.
Calculate Metrics: Compute the selected performance metrics (e.g., Accuracy, F1, RMSE) for both models based on their predictions on $D_{test\_real}$ . You will have pairs of scores, such as $Accuracy_{real}$ and $Accuracy_{synth}$ , $F1_{real}$ and $F1_{synth}$ , etc.

Interpreting the Results

The comparison boils down to analyzing the difference between the metrics obtained from the real-data-trained model and the synthetic-data-trained model.

Direct Comparison: Look at the absolute difference: $Metric_{real} - Metric_{synth}$ . A small difference suggests the synthetic data preserves the utility for this task well.
Performance Ratio: Calculate the ratio: $\frac{Metric_{synth}}{Metric_{real}}$ $\frac{M e t r i c _{sy n t h}}{M e t r i c _{re a l}}$ . This provides a normalized view.
- A ratio close to 1.0 (e.g., 0.95 to 1.05) indicates that the synthetic data provides nearly equivalent utility to the real data for training this specific model on this specific task.
- A ratio significantly below 1.0 (e.g., 0.8) suggests a noticeable drop in performance when using synthetic data. Whether this drop is acceptable depends on the application's tolerance and the benefits gained from using synthetic data (e.g., privacy, data augmentation).
- A ratio significantly above 1.0 is unusual but could potentially occur if the synthetic data generation process somehow regularizes the model or emphasizes important patterns more clearly than the available real training data. This warrants further investigation.

Visualizations are often helpful for comparing multiple metrics simultaneously.

Comparison of key classification metrics for models trained on real vs. synthetic data and evaluated on a real test set. Ratios here are approximately 0.95 for Accuracy, 0.94 for F1-Score, and 0.96 for AUC.

It's important to repeat this process potentially with different downstream model types, as some models might be more sensitive to imperfections in the synthetic data than others. A synthetic dataset might yield good results for a linear model but perform less adequately for a complex deep learning model, or vice-versa.

Ultimately, comparing these downstream performance metrics provides a tangible, task-oriented measure of your synthetic data's utility. It answers the question: "Can I use this synthetic data to train a model that performs adequately on real-world tasks?"