# Challenges of Using Synthetic Data Generation Methods for Tabular Microdata
## 3 Results
The Copula model results indicate moderate performance, with accuracies of 0.808 \(\pm\) 0.021 for the AQ dataset, 0.400 \(\pm\) 0.056 for the AP dataset, and 0.604 \(\pm\) 0.072 for the BC dataset. These results are generally lower compared to the original data and some GAN-based models, highlighting the challenges in capturing intricate data patterns with simpler statistical models. Specifically, for the AQ dataset, the accuracy is reasonably high compared to other models. On the AP dataset, the performance is notably lower, which is probably due to the higher number of categorical features, which must be transformed to continuous ones. The Copula model struggles to capture the underlying relationships as effectively as GAN-based models. On the BC dataset, the Copula model achieves an accuracy that is also significantly lower than the original model's 0.880 \(\pm\) 0.006. The higher feature count likely exacerbates the model's limitations in capturing complex dependencies. The characteristics of each dataset--such as the number of instances, features, and the mix of numerical and categorical features--play a crucial role in determining model performance. The AQ dataset, with 661 instances and 12 features, represents a regression task that generally showed better performance with models like TVAE and CopulaGAN when sufficient training epochs were used. The AP dataset, with 2345 instances and 17 features, presented more challenges, likely due to its higher feature count and mixed numerical and categorical data, leading to more varied model performance. The BC dataset, with 455 instances and 31 features, performed consistently well across models, indicating that it is indeed the number of categorical data that poses the highest difficulty. Next, we highlight the differences between the high-dimensional datasets MU and MB and the other datasets (AP, AQ, BC). The baseline performance on the MB dataset is notably low, reflecting its complexity. This complexity results in poor performance across most SDG models, with TVAE being a notable exception. TVAE demonstrated relatively robust performance, particularly with a high number of categorical variables. The best results for TVAE were obtained with the highest number of epochs, although it should be noted that training for 10,000 epochs with a batch size of 60 did not finish in under 60 h. For the MU dataset, the original performance is relatively high, and the results are comparable to those obtained from the low-dimensional datasets. This suggests that while the total number of columns is a factor, the number of categorical columns is the primary challenge in SDG. Interestingly, this observation is not reflected in the results from the Copula model. While Copula performed poorly on the MU dataset, it was the second-best-performing model on the MB dataset after TVAE. This indicates that the Copula model's ability to recognize interdependencies in continuous data can partially compensate for the difficulties posed by categorical variables. The contrasting performance of the Copula model on MU and MB datasets underscores the need for models that can effectively manage both continuous and categorical data interdependencies. In our comparative evaluations, TVAE demonstrates a higher capability of achieving this outcome than traditional GAN models. Figure 1 presents scatter plots illustrating the relationship between \(\varepsilon\)-Identifiability and RF-utility across five different datasets (see also Table A2 for the individual \(\varepsilon\)-Identifiability values). The plots use different symbols to represent various batch sizes: circles for 0, stars for 60, and diamonds for 500. Colors indicate different models: red for CTGAN, green for Copula, blue for CopulaGAN and purple for TVAE. The color intensity corresponds to the number of epochs, with lighter colors for fewer epochs and darker colors for more epochs.