## 4 Discussion  
In the evaluation results of this study, the predictive performance of the models trained only with soft label information \(\mathrm{X_{pdf}}\) were not always better than that of the models trained with only input data \(\mathrm{X}\) (Table 1 vs. Tables 3 and 5 vs. Table 7). On the other hand, regardless of the matching ratio of patients and control samples, we found that as long as the soft label information \(\mathrm{X_{pdf}}\) was combined with the input data \(\mathrm{X}\) to train the prediction models, the evaluation indicators PPV and TPR for identifying positive test samples were improved. At the same time, the indicators NPV and TNR for identifying negative samples were also advanced (Table 2 vs. Tables 3 and 6 vs. Table 7). In order to quantitatively evaluate whether the prediction performance of the learning models constructed using both \(\mathrm{X}\) and \(\mathrm{X_{pdf}}\) was better than that of the models constructed using \(\mathrm{X}\) only, we computed the OR and corresponding 95% CI values for performance measures of accuracy, PPV, and TPR. For patients and controls with a matching ratio of 1:1, it was found that the OR values of accuracy ranged from 2.045 to 0.996. Similarly, the OR values of PPV ranged from 1.410 to 0.983, and those of TPR ranged from 4.427 to 0.839 (Table 4). It was verified that most of the learning models constructed using both \(\mathrm{X}\) and \(\mathrm{X_{pdf}}\) performed better in terms of accuracy, PPV, and TPR than models constructed using \(\mathrm{X}\) only. In other words, the appending use of soft label information \(\mathrm{X_{pdf}}\) can improve the accuracy of prediction models in identifying bipolar disorder patients. At the same time, increased PPV values represented fewer false positive samples, whereas increased TPR values represented the identification of more potential positive samples. On the other hand, for cases and controls with a matching ratio of 1:3, it was found that the OR values of accuracy ranged from 2.048 to 1.071. Similarly, the OR values of PPV ranged from 4.181 to 0.691, and those of TPR ranged from 8.362 to 0.889 (Table 8). Consequently, we can still conclude that most of the learning models constructed using both \(\mathrm{X}\) and \(\mathrm{X_{pdf}}\) performed better than models constructed using X only. In this study, we used medical history information that was readily available from the electronic health record system to try to improve on the limitation of previous studies that needed to use special instruments to obtain data. In addition, we introduced the concept of knowledge distillation and combined KDE and other machine learning algo \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **OR for Accuracy** & **OR for PPV** & **OR for TPR** \\ \hline \multicolumn{4}{c}{\(\mathrm{X_{pdf}}\) was generated using the Gaussian kernel.} \\ \hline SVM & 1.283 (1.447–1.138) & 0.691 (0.779–0.613) & 8.025 (9.049–7.117) \\ Decision tree & 1.108 (1.252–0.981) & 1.139 (1.286–1.008) & 1.138 (1.286–1.008) \\ NN (80, 10, 1) & 1.258 (1.436–1.102) & 1.653 (1.887–1.447) & 0.889 (1.015–0.778) \\ NN (160, 40, 1) & 1.071 (1.206–0.951) & 1.069 (1.203–0.949) & 1.369 (1.542–1.216) \\ NN (80, 20, 10, 1) & 2.048 (2.408–1.742) & 4.181 (4.916–3.556) & 1.523 (1.790–1.295) \\ \hline \multicolumn{4}{c}{\(\mathrm{X_{pdf}}\) was generated using the exponential kernel.} \\ \hline SVM & 1.296 (1.461–1.149) & 0.695 (0.783–0.616) & 8.362 (9.429–7.416) \\ Decision tree & 1.071 (1.209–0.949) & 1.092 (1.232–0.967) & 1.089 (1.229–0.965) \\ NN (80, 10, 1) & 2.042 (2.363–1.765) & 2.446 (2.831–2.114) & 2.355 (2.725–2.035) \\ NN (160, 40, 1) & 1.216 (1.378–1.074) & 1.311 (1.484–1.157) & 1.210 (1.370–1.068) \\ NN (80, 20, 10, 1) & 1.187 (1.340–1.051) & 1.191 (1.345–1.055) & 1.304 (1.472–1.155) \\ \hline \hline \end{tabular}
\end{table}