## 4 Discussion

Table 8: The OR and corresponding 95% CI values between the learning model constructed using both \(\mathrm{X}\) and \(\mathrm{X_{pdf}}\) (Table 6) and the model constructed using \(\mathrm{X}\) only (Table 7) for patients and controls with a matching ratio of 1:3.  
rithms to train the diagnosis models of bipolar disorder. For patients and controls with a matching ratio of 1:1, the evaluation results of our diagnosis models yielded an accuracy of 0.810-0.659, a PPV of 0.806-0.700, an NPV of 0.846-0.626, a TPR of 0.854-0.524, and a TNR of 0.808-0.705 (Tables 1-3). The mean values of these metrics were an accuracy of 0.774, a PPV of 0.764, an NPV of 0.786, a TPR of 0.787, and a TNR of 0.761. Moreover, for patients and controls with a matching ratio of 1:3, the evaluation results of our prediction models yielded an accuracy of 0.894-0.746, a PPV of 0.862-0.493, an NPV of 0.924-0.775, a TPR of 0.773-0.502, and a TNR of 0.981-0.807 (Tables 5-7). The mean values of these metrics were an accuracy of 0.808, a PPV of 0.629, an NPV of 0.871, a TPR of 0.610, and a TNR of 0.875. Referring to the review of 33 studies based on machine learning models used to diagnose patients with bipolar disorder, the evaluation measure of accuracy is reported in 24 studies. The values range from 0.98 to 0.64, and the mean value is 0.8206. Moreover, the measure of TPR is reported in 15 studies. The values range from 0.875 to 0.664, and the mean value is 0.7826. Finally, the measure of TNR is reported in 13 studies. The values range from 0.971 to 0.742, and the mean value is 0.854 [6]. These past studies used different types of data and various machine learning algorithms to construct predictive models for bipolar disorder, and the sizes of the datasets they collected also varied greatly. Therefore, we cannot directly compare the measured values to evaluate predictive performance. However, in the performance metrics of accuracy, TPR, and TNR, the prediction models we constructed obtained mean values close to the results of past studies. There is obvious overlap in the value ranges of these performance measures. It is worth noting that the analysis data of previous studies require special medical instruments to be obtained, but our study instead used medical history information that was readily available from the electronic health record system and achieved similar results of prediction performance. This verifies that we can construct effective identification models for bipolar disorder patients using medical history data and various machine learning algorithms. Furthermore, in view of the fact that most previous studies had sample sizes of less than 1000, we collected tens of thousands of data samples to improve the representativeness of the constructed prediction models. In order for knowledge distillation to improve the prediction performance of the trained model, the soft label information must provide accurate distribution conditions of the input data. Referring to the research work of [PERSON] et al., they argued that the probability distribution values produced by a deep learning model can be transferred to a shallow \"distilled\" learning model [13]. In addition, the research work of [PERSON] et al., found that the final outcomes of the student network can be thought of as approximating the conditional probabilities provided by the teacher group [11]. Since it is known that KDE has been applied in estimating the conditional probability distributions of input data when using a naive Bayes classifier [16; 27], our study was inspired to combine KDE for knowledge distillation to construct prediction models for bipolar disorder. Furthermore, when KDE is used for data analysis, the setting of bandwidth has a great influence on the accurate estimation of data distributions. There have been numerous studies discussing the criteria to set this parameter [14; 15; 28]. A novel KDE method has been proposed to minimize the bias part of the mean square error and to elevate the bandwidths of the kernel functions to alleviate the effects of variance.