## 5 Experiments
### Quantitative and Qualitative Evaluation  
The results obtained were also subjected to comparative analysis with those of the intermediate models developed during the design phases. This comparison aims to clarify the contribution of each architectural development, from the transition of the convolutional layers to the GRUs to the integration of MCMC sampling. The analysis was further enriched by a direct comparison of the final model with the results reported in the scientific literature, in particular regarding the TimeGAN model. This was achieved using the same evaluation metrics (discriminative score, predictive score), ensuring rigorous and transparent comparability. This approach is advantageous in assessing the competitiveness of the final model against established state-of-the-art methods, and in assessing its position concerning existing solutions.  
Quantitative metrics are essential tools for objectively assessing the performance of a generative model. Moreover, these facilitate the rigorous assessment of the quality of synthetic data produced by comparing them with real data on several relevant criteria, including their statistical consistency, their capacity to preserve temporal relationships, and their utility in practical applications.  
Two types of quantitative metrics are used:  
* The discriminative score: This metric quantifies the capacity of a discriminative classifier, trained on a mixed dataset comprising synthetic and real samples, to differentiate between the two classes. The score is defined as \((accuracy-0.5)\), and its value is set within a range between 0 and 1, wherein a value closer to 0 signifies that it is difficult to distinguish the generated data from the original data and so is a better model.
* The predictive score: This metric assesses the ability of the synthetic data to maintain the predictive relationships present in the real data. The calculation is based on a predictive model trained on the synthetic dataset and then tested on the real one. The sequence model, which aims to predict next-time vectors, is an N-layer GRU evaluated using the mean absolute error on the original dataset. Again, the range of values is defined between 0 and 1, with a lower value indicating a higher quality of synthetic data.  
These comparison metrics were all considered in [11], and the authors' available code for these metrics has been used ([[https://github.com/jsyoon0823/TimeGAN](https://github.com/jsyoon0823/TimeGAN)]([https://github.com/jsyoon0823/TimeGAN](https://github.com/jsyoon0823/TimeGAN)) accessed on 4 January 2025).  
The results presented in Table 2 demonstrate that integrating a GRU and MCMC into VAE models enhances the quality of the synthetic data generated, as evidenced by both the discriminative score and predictive score. In particular, incorporating a GRU layer into the VAE architecture has been observed to improve the model's capacity to generate samples that are more closely aligned with the characteristics of real data, as reflected by a reduction in the discriminator score. Nevertheless, the VAE with MCMC sampling exhibits the mostnotable performance, demonstrating the capacity to represent intricate temporal dynamics and generate synthetic data of superior quality and consistency with real data.