## 5 Experiments
### SAS vs. RAS Under Limited Data Availability  
Another set of experiments was conducted to compare the performance of RAS and SAS under conditions of limited data availability. In these experiments, we used the same five Algorithms, each fine-tuned on data from \(\mathbb{D}_{t}\) for five epochs. The amount of validation data from \(\mathbb{D}_{V}\) used in each run was reduced to 50 images per class. We performed 10 runs of the experiment for both RAS and SAS. The results are presented in Table 3. For each RAS run, eight Algorithm selectors were trained on 50 randomly sampled images from \(\mathbb{D}_{V}\). For each SAS run, we used the same 50 images selected for RAS as the seed dataset \(\mathbb{D}_{E}\) to train a GAN. This ensured that neither RAS nor SAS had an advantage in data sampling. For each run, the GAN was trained independently with a distinct fixed random seed. For five of the runs, we used the Inception Score (IS) to select the generator training epoch for data generation, and for the other five runs, we used the Frechet Inception Distance (FID). The results show that the difference between using IS and FID for generator epoch selection was not statistically significant for this set of experiments. Using the selected generator epoch, 1000 synthetic images per class were generated for each run. The Algorithm selectors for SAS were trained on the generated synthetic images, and the final classification accuracy after Algorithm selection was recorded. The \"Best Classifier\" row reports the average result of the best-performing classifier from each run. The \"Average\" row shows the mean accuracy of all eight Algorithm selectors across all runs. For each Algorithm selector, we report the mean accuracy along with the 95% confidence interval computed across 10 runs. We performed paired \(t\)-tests between RAS and SAS results for each Algorithm selector. A p-value less than 0.05 indicates a statistically significant difference between RAS and SAS. A p-value greater than 0.05 suggests that the difference is not statistically significant. Some Algorithm selectors performed very consistently despite being trained on different data with varying random seeds. However, the distribution of test results violated the normality assumption required for the paired \(t\)-test for several models: SVM, KNeighborsClassifier, SGDClassifier, LogisticRegression, RandomForestClassifier, MLPClassifier, and Best Classifier. Therefore, we also performed the Wilcoxon signed-rank test as a non-parametric alternative to paired \(t\)-tests. The results showed a statistically significant improvement for SVM, LogisticRegression, RandomForestClassifier, and MLPClassifier when trained on synthetic data compared to real data. Conversely, DecisionTreeClassifier showed a statistically significant decrease in performance under the same condition. KNeighborsClassifier \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm Selector** & **Avg. RAS** & **Avg. SAS** & **\(\Delta\) (SAS \(-\) RAS)** & **p (\(t\)-Test)** & **p (Wilcox)** \\ \hline ExtraTreesClassifier & \(88.38\pm 1.18\) & \(89.43\pm 0.96\) & 1.054 & 0.0613 & 0.0273 \\ \hline SVM & \(89.39\pm 0.53\) & \(90.77\pm 0.05\) & 1.378 & 0.0004 & 0.0139 \\ \hline DecisionTreeClassifier & \(90.70\pm 0.20\) & \(88.77\pm 0.89\) & \(-1.930\) & 0.0003 & 0.0020 \\ \hline KNeighborsClassifier & \(90.88\pm 0.13\) & \(90.66\pm 0.42\) & \(-0.220\) & 0.2729 & 0.1394 \\ \hline SDCLassifier & \(88.33\pm 0.75\) & \(89.10\pm 0.82\) & 0.767 & 0.1545 & 0.1394 \\ \hline LogisticRegression & \(87.67\pm 0.82\) & \(89.25\pm 0.76\) & 1.580 & 0.0030 & 0.0139 \\ \hline RandomForestClassifier & \(89.65\pm 0.32\) & \(90.35\pm 0.52\) & 0.703 & 0.0020 & 0.0273 \\ \hline MLPClassifier & \(88.07\pm 2.23\) & \(89.85\pm 0.56\) & 1.775 & 0.1530 & 0.0273 \\ \hline Best Classifier & \(90.92\pm 0.13\) & \(90.99\pm 0.25\) & 0.066 & 0.6275 & 0.1094 \\ \hline Average & \(89.13\pm 0.17\) & \(89.77\pm 0.27\) & 0.639 & 0.0028 & 0.0020 \\ \hline \hline \end{tabular}
\end{table}