## 3 Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Algorithm** & **TP** & **FP** & **TN** & **FN** & **Accuracy** & **PPV** & **NPV** & **TPR** & **TNR** \\ \hline \multicolumn{10}{c}{X\({}_{\text{pdf}}\) was generated using the Gaussian kernel.} \\ \hline SVM & 1641 & 509 & 1497 & 353 & 0.785 & 0.763 & 0.809 & 0.823 & 0.746 \\ Decision tree & 1384 & 592 & 1414 & 610 & 0.700 & 0.700 & 0.699 & 0.694 & 0.705 \\ NN (80, 10, 1) & 1549 & 566 & 1425 & 336 & 0.767 & 0.732 & 0.809 & 0.822 & 0.716 \\ NN (160, 40, 1) & 1512 & 516 & 1466 & 459 & 0.753 & 0.746 & 0.762 & 0.767 & 0.740 \\ NN (80, 20, 10, 1) & 1540 & 384 & 1485 & 536 & 0.767 & 0.800 & 0.735 & 0.742 & 0.795 \\ \hline \multicolumn{10}{c}{X\({}_{\text{pdf}}\) was generated using the exponential kernel.} \\ \hline SVM & 1626 & 498 & 1508 & 368 & 0.784 & 0.766 & 0.804 & 0.815 & 0.752 \\ Decision tree & 1371 & 561 & 1445 & 623 & 0.704 & 0.710 & 0.699 & 0.688 & 0.720 \\ NN (80, 10, 1) & 1597 & 500 & 1468 & 306 & 0.792 & 0.762 & 0.828 & 0.839 & 0.746 \\ NN (160, 40, 1) & 1551 & 549 & 1447 & 349 & 0.770 & 0.739 & 0.806 & 0.816 & 0.725 \\ NN (80, 20, 10, 1) & 1566 & 509 & 1489 & 358 & 0.779 & 0.755 & 0.806 & 0.814 & 0.745 \\ \hline \end{tabular}
\end{table} 
Table 1: The evaluation results of the test set on prediction models of bipolar disorder trained using various learning algorithms for patients and controls with a matching ratio of 1:1; only the soft label information \(X_{\text{pdf}}\) was used as input attributes. Figure 2: The respective probability density functions estimated by KDE of patients and control samples with a matching ratio of 1:1. Finally, in order to verify the effectiveness of the soft label information \(\mathrm{X_{pdf}}\), only data X were used as attributes for training and validating the prediction models. The evaluation results for the test set are shown in Table 3.  
Comparing the results shown in Tables 1 and 3, it can be seen that only using the soft label information \(\mathrm{X_{pdf}}\) as the input attributes did not always improve the performances of the predictive models. On the other hand, in order to quantitatively evaluate whether the prediction performance of the learning models constructed using both X and \(\mathrm{X_{pdf}}\) (Table 2) was better than that of the models constructed using X only (Table 3), we adopted the concept of the odds ratio (OR). We focused on the performance of the prediction models in correctly identifying positive samples, that is, bipolar disorder patients. Therefore, the definition formulas of these evaluation metrics are described as follows. \[\text{OR for PPV}=\frac{\left(\frac{TP_{1}}{FP_{1}}\right)}{\left(\frac{TP_{ 2}}{FP_{2}}\right)}\]  
\[\text{OR for TPR}=\frac{\left(\frac{TP_{1}}{FN_{1}}\right)}{\left(\frac{TP_{ 2}}{FN_{2}}\right)}\]  
\[\text{OR for accuracy}=\frac{\left(\frac{TP_{1}+TN_{1}}{(FP_{1}+FN_{1})}\right) }{\left(\frac{TP_{2}+TN_{2}}{(FP_{2}+FN_{2})}\right)}\]  
Among these formulas, the variables \(TP_{j}\), \(FP_{j}\), \(TN_{j}\), and \(FN_{j}\) represent the prediction results of a true positive, false positive, true negative, and false negative output, respectively, by model \(j\). The OR and corresponding 95% confidence interval (CI) values of the evaluation