## 2 Materials and Methods
### Methods
#### 2.2.3 Prediction Methods  
We used three types of prediction methods--statistical method, machine learning method, deep learning method. * Multiple linear regression  
Multiple linear regression is an extension of simple linear regression. It is a regression used when there are two or more explanatory variables, and is expressed as shown in Equation (1) below. \[y_{i}=\beta_{0}+\beta_{1}x+\beta_{2}x_{i2}+\cdots+\beta_{p}x_{ip}+\epsilon_{i} \,\epsilon_{i}\sim N(0,\ \sigma^{2})\ i=1,2,\ \cdots,n \tag{1}\]  
where \(\beta_{0},\ \beta_{1},\ \cdots,\ \beta_{p}\) are the regression coefficients in the form of constant values, \(\epsilon_{i}\) is the unexplained error, and \(x_{ip}\) is the \(i\)-th observation value of the \(p\)-th explanatory variable. * Support vector machine (SVM)  
The basic idea of SVM [28] is to classify data by creating a hyperplane. While it is well distinguished in a linear problem, additional work using the kernel function in high-dimensional problems such as nonlinear problems. The optimal hyperplane is determined in a way that maximizes the margin. That is, the hyperplane with the largest distance from  
Figure 4: (\(k=3\)) K-nearest neighbor imputation. the data is selected. In the case of regression data, the hyperplane is the regression line. Figure 5 shows a support vector machine with two variables. * Ensemble tree  
Ensemble tree is a method of applying ensemble, which is a method of making better generalization performance by connecting multiple classifiers into a single meta-classifier, to a decision tree. Here, the decision tree is an analysis method that charts decision rules in a tree-like structure. 1. Random forest  
Random forest [29] is a type of ensemble learning method that uses multiple decision trees constructed during the training process to classify or predict datasets. That is, it is an ensemble of decision trees that improves generalization performance and reduces overfitting by averaging several (deep) decision trees to solve the problem of the large variance in individual trees. Random forests are not as easy to interpret as decision trees, but they generally do not require pruning (a way to simplify the model), necessitating less effort for tuning. Additionally, they have fewer hyperparameters (number of trees, bootstrap size, number of variables to be selected in each split). Figure 6 is an example of the random forest with \(k\) decision trees. 2. Extremely randomized tree (Extra Tree)  
Extra Tree is a method constructed using the ensemble method of a non-pruned decision tree or regression tree [23]. It is similar to the random forest method, however, while random forest uses sampling without replacement when creating multiple trees based on bootstrap, Extra Tree uses sampling with replacement and uses Whole Original data. In addition, random forest calculates the information gain for all features in the split process and splits based on this value; however, in the case of Extra Tree, the split is performed by randomly selecting a variable when performing the split process. Therefore, it saves computation time compared to random forest, and reduces bias and variance by performing splits randomly. 3. XGBoost (extreme gradient boosting) is a modified method of gradient boosting machine (GBM) [30] and is in the form of a tree to which gradient boosting is applied. The biggest advantage of XGBoost is that parallel processing is possible and the amount of computation is reduced. In addition, overfitting can be prevented by shrinkage and column subsampling, Additionally, by using the approximate algorithm, Weighted Quantile Sketch, and Sparsity-aware Split Finding method instead of the Exact Greedy Algorithm for the  
Figure 5: Support vector machine with two variables. split operation, the calculation speed is increased, allowing excellent performance results to be obtained even for datasets with many missing values and zeros [31]. * Deep neural network (DNN)  
DNN is a learning method based on ANN. That is, it is an ANN with multiple hidden layers.