## 3 Results
### Validation Results
#### 3.2.2 Evaluating the Practicability of Data Augmentation
 } \\ \cline{3-3} \cline{5-7}  & & \multicolumn{2}{c}{**Correlation Coefficient**} & & & \\ \cline{2-7}  & & **Pearson** & **Spearman** & **Pearson** & **Spearman** \\ \hline
**Pairs of Data Types** & **Compared Data** & **r** & **rho** & **r** & **rho** & \\ \hline Benchmark & Real (original) & 1.000 *** & 1.000 *** & 1.000 *** & 1.000 *** & 1.000 \\ \hline \multirow{6}{*}{Original real data vs. Nonaugmented data & Real (seed) & 0.751 *** & 0.723 *** & 0.646 *** & 0.683 *** & 0.701 \\ \cline{2-7}  & Synthesized (CTGAN) & 0.735 *** & 0.555 *** & 0.737 *** & 0.747 *** & 0.694 \\ \cline{2-7}  & Synthesized (TVAE) & 0.672 *** & 0.684 *** & 0.401 * & 0.704 *** & 0.615 \\ \cline{2-7}  & Synthesized & (CopulaGAN) & 0.634 *** & 0.720 *** & 0.820 *** & 0.702 *** & 0.732 \\ \hline \multirow{6}{*}{Original real data vs. Augmented data} & Real (original) + Synthesized & 0.821 *** & **0.881 *** & **0.849 *** & **0.837 *** & **0.847** \\ \cline{2-7}  & Real (original) + Synthesized & **0.779 *** & **0.859 *** & **0.886 *** & **0.890 *** & **0.854** \\ \cline{2-7}  & Real (original) + Synthesized & 0.020 & 0.669 *** & 0.839 *** & 0.710 *** & 0.560 \\ \cline{2-7}  & Real (seed) + Synthesized & 0.767 *** & 0.518 *** & 0.706 *** & 0.717 *** & 0.677 \\ \cline{2-7}  & Real (seed) + Synthesized & & & & & \\ \cline{2-7}  & Real (seed) + Synthesized & 0.718 *** & 0.692 *** & 0.46 * & 0.745 *** & 0.654 \\ \cline{2-7}  & Real (seed) + Synthesized & & & & & \\ \cline{2-7}  & (TVAE) & 0.718 *** & 0.692 *** & 0.46 * & 0.745 *** & 0.654 \\ \cline{2-7}  & Real (seed) + Synthesized & & & & & \\ \cline{2-7}  & Real (seed) + Synthesized & & & & & \\ \cline{2-7}  & (TVAE) & 0.718 *** & 0.692 *** & 0.46 * & 0.745 *** & 0.654 \\ \cline{2-7}  & Real (seed) + Synthesized & & & & & \\ \cline{2-7}  & Real (seed) + Synthesized & & & & & \\ \cline{2-7}  & (TVAE) & 0.858 *** & 0.765 *** & 0.839 *** & 0.710 *** & 0.725 \\ \hline \multirow{6}{*}{ \begin{tabular}{c} **\(p<0.001\) ** \\ **\(p<0.001\) \\ **\end{tabular}  } & \multicolumn{2}{c}{**\(p<0.01\). * \(p<0.05\). The bold and underlined values express the best performances, the bold values express the second-ranked performances, and the underlined values express the third-ranked performances in each column in each data pair. **} \\ \cline  
predictive performance vs. concordance of the feature importance score map (Figure 9B) was created based on \"Averaged value of evaluation metrics\" in Table 2 and \"Averaged correlation coefficients\" in Table 4. Regarding the averaged correlation coefficient values of the original datasets in Table 4 and Figure 9B, we provided them with 1.00 because we defined them as the benchmark value. From the results of both maps, both augmented and synthesized datasets had higher predictive performance than real datasets, regardless of the data scale. The result of the actual predictive performance vs. stability map (Figure 9A) showed that the augmented and synthesized datasets achieved higher predictive performances than the two real datasets (the original and seed datasets), relatively lower fluctuation than the original dataset, and much lower fluctuation than the seed dataset. Two augmented datasets (\"Real (seed) + Synthesized (CTGAN)\" and \"Real (seed) + Synthesized (CopulaGAN)\") and two synthesized datasets (\"Synthesized (CTGAN)\" and \"Synthesized (CopulaGAN)\") were placed in desirable positions because they yielded high predictive performance and universality regardless of machine learning algorithms. However, the augmented and synthesized datasets had the same or relatively low averaged correlation coefficient values as the seed datasets, unlike the predictive performance.