## 5 Experiments
### Algorithm Selection as a Function of Algorithm Selectors  
The next set of experiments shows the performance of the individual Algorithm selectors. Figure 8 shows the accuracy of classification when the Algorithm selector is trained on synthetic samples from \(\mathbb{D}_{S}\) generated by GAN from an increasing number of seed samples \(\mathbb{D}_{E}\) which are selected from \(\mathbb{D}_{V}\) and \(\mathbb{D}_{t}\).  
As shown in Figure 3, the training dataset used here is constructed in a similar fashion of constructing the sample dataset \(\mathbb{D}_{E}\). This means that only the first samples from \(\mathbb{D}_{V}\) are used, and when their number is larger than \(|\mathbb{D}_{V}|\), samples from \(\mathbb{D}_{t}\) are used. However, all seed images are real and all Algorithm selectors are trained on synthetic images generated by the GAN network.  
Figure 8 shows that for each size of seed dataset \(\mathbb{D}_{E}\), different Algorithm selectors provides the highest classification accuracy. Because of this observation, we will further  
Figure 7: Example images used for our experiments. (**a,b**) real images; (**c,d**) synthetic images for healthy subjects; and (**e,f**) synthetic images for patients with pneumonia. (**a**) Example of real X-rays of healthy subjects; (**b**) Example of real X-rays of patients with pneumonia; (**c**) example of synthetic X-rays for healthy subjects (highest FID score); (**d**) example of synthetic X-rays for healthy subjects (highest IS score); (**e**) example of synthetic X-rays for patients with pneumonia (highest FID score); (**f**) example of synthetic X-rays for patients with pneumonia (highest IS score).  
report only the best performance for each experiment by selecting the most accurate Algorithm selector for each task.  
Note that as expected, the more images are used to generate the \(\mathbb{D}_{S}\) dataset, the higher the Algorithm selection accuracy is in average. Interestingly, the variation is lowest for \(70\leq|\mathbb{D}_{E}|\leq 300\). The implication of this observation is that for very few samples in \(\mathbb{D}_{E}\), GAN-generated synthetic images are too noisy, while for a very large amount in \(\mathbb{D}_{E}\), the generated images do not provide enough variation for all the Algorithms used by the algorithm selector, and thus resulting in almost no classification accuracy increase. However, an interesting observation is that the variation between the classification accuracy of the different Algorithm selectors is also very small when only 10 images are used to seed the GAN generator.  
Figure 9 summarizes these results. The plots show the average (Avg.) and most accurate (Best) Algorithm selection accuracies. The average accuracy represents the average over the set of all nine Algorithm selectors. The average is computed over the set of Algorithm selectors trained on the same set of training samples and plots them against the most accurate Algorithm selector for both RAS and SAS approaches. The Algorithm selectors were trained on increasing number of real or synthetic images and the most accurate result for each type of learning is displayed. The classification accuracy was evaluated on 228 real images per class. Note that Algorithm selection trained on synthetic images outperforms or equals Algorithm selection trained on real images on five out of six data points (red line).  
Figure 8: The average accuracy of Algorithm selectors on the classification task as a function of number of seed samples of GAN.  
Figure 9: Processing accuracy on 200 real images for best and average Algorithm selection trained on real and synthetic images.  
Another observation is that the Algorithm selection provides the highest accuracy when the Algorithm selection provides the highest degree of noise. Here, it means that the Algorithm selection is trained on smallest number of samples (10 in Figure 9) in \(\mathbb{D}_{S}\).