## 4 Results
### Accuracy of Synthetic Data Generation
#### 4.1.1 Statistical Analysis  
In this work, we used two sets of methods to analyze our synthetic AF and CE data; the \"evaluate quality\" function [42] of SDV single table and the Mann-Whitney test [43]. Table 3 displays the quality function results. Below, we provide a detailed interpretation of the results and their implications:  
* Column shapes (for single columns of data and is often called the marginal distribution of each column): While these values may appear slightly lower than other metrics, they still indicate a strong resemblance between real and synthetic column distributions. * Column pair trends (for pair of columns and is the correlation or bivariate distribution of columns): These high percentages indicate that relationships and dependencies between pairs of columns (e.g., correlations) in the synthetic data closely mimic those in the real data. This demonstrates that the structural integrity of the dataset is preserved, which is critical for maintaining its utility in downstream tasks like machine learning model training. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Model: “Keras Sequential”**} \\ \hline
**Layer (type)** & **Output Shape** \\ Input layer (Dense) & ( 64) \\ Activation (Activation) & ( 64) \\ Hidden layer 1 (Dense) & ( 32) \\ Activation (Activation) & ( 32) \\ Dropout 1 (Dropout) & ( 32) \\ Output layer (Dense) & ( 1) \\ \hline \multicolumn{2}{c}{**Trainable params: 2113**} \\ \hline
**Non-trainable params: 4160** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cardiovascular event (CE) model architecture summary. Computational complexity analysis of the transfer learning architecture: by freezing the earlier layers, gradients need only be computed for the newly added (unfrozen) layers. Thus, if \(D^{\prime}\) is the input dimensionality fed into the first unfrozen layer and \(H^{\prime}\) is the size of the newly added layers, the computational complexity per epoch reduces to \(\mathcal{O}(N\cdot D^{\prime}\cdot H^{\prime})\). Over \(E\) epochs, it becomes \(\mathcal{O}(E\cdot N\cdot D^{\prime}\cdot H^{\prime})\). This maintains a linear scaling with the number of samples, epochs, and the size of the unfrozen portion of the model. Overall score: These scores combine multiple aspects of statistical similarity and indicate a strong match between real and synthetic datasets. An overall score above 85% provides confidence that the generated data retain the key representational features of the real data, while reducing risks associated with direct data sharing. Within the Open-CESP initiative, a key aspect of synthetic data utility lies in its capacity to mirror the statistical characteristics of the original data. This necessitates a significant degree of distributional similarity between the synthetic data and the original dataset [44]. When generating synthetic data, it is crucial to balance the resemblance to the original data with privacy requirements. While a higher similarity enhances usability in practical applications, the generated data must differ enough to prevent leakage of sensitive information. This balance, often referred to as \"realism\" or \"resemblance\", is validated through statistical comparisons and expert qualitative assessments to ensure the synthetic data are both plausible and privacy-preserving [45]. We considered these critical points in our approach, and the reported statistical similarities between the real and synthetic datasets for AF and CEs highlight our commitment to effectively addressing both utility and privacy requirements. The Mann-Whitney test was used to investigate the differences in HRV parameters. The median, interquartile range (IQR), and \(p\)-value were estimated for each parameter. We did not interpret the Mann-Whitney U test's results as direct \"quality scores\", instead, \(p\)-values indicated whether there was a statistically significant difference between the synthetic and real data distributions for each feature.