## 3 Results
### Prediction Results of Single Model  
This article chooses to include the following models: linear regression (LR), which is very important in solving regression problems; random forest (RF) and extremely randomized trees (ExtraTrees), which use the bagging ensemble learning method; gradient-boosted decision tree (GBDT); extreme gradient boosting (eXtreme gradient boosting; XGBoost); and categorical boosting (CatBoost), which use gradients with the boosting ensemble learning method to improve decision trees. The ensemble learning of bagging and boosting has achieved good results in other fields. SVM (support vector machine) can obtain much better results than other algorithms can on small-sample training sets and has unique advantages in the performance of high-dimensional regression problems. KNN also has good practical application effects because of its mature theory and efficient training. All selected models are supported by rigorous mathematical theory. All models were implemented and optimized in Python 3.7. The operating system is a 64-bit Windows 7 with a quad-core Intel Core I7 CPU @ 2.6 GHz (8 cpus) and 8.00 GB of RAM.  
First, it is necessary to optimize the parameters of each monomer base model to achieve the optimal prediction effect. In this paper, random and grid searches are used to optimize the parameters to improve the training speed and accuracy. The essence of the grid search method is to divide all the parameters to be searched into a grid with the same length according to the established space search scope and the proposed coordinate system. Next, a random search is used to select the best point for rough search with stride length in a large range. Then, a smaller step size is used to search the grid near the best advantage to select the optimal solution and repeat the above steps. The model's generalization ability is further improved through eight-fold cross validation to avoid overfitting.  
The optimal parameters of each model are shown in Table 8. Statistical indicators are calculated on the test set to evaluate the predictive performance of these eight models. The prediction and evaluation results are shown in Table 9. For high-dimensionality and small-sample regression quality prediction, SVR and linear regression perform the best among the eight models. According to each statistical indicator, the RMSE of the SVR prediction result is 0.0788, which is the smallest among all models. The MAE of the linear regression prediction result is 0.0619, which is the smallest among all models. In the test set, the SVR and linear regression model \(R^{2}\) is the highest, reaching 0.8883. KNN performed the worst, with \(R^{2}\) of 0.6593. Except for RandomForest and KNN, all other models have \(R^{2}\) above 0.8.  
The error of each model is shown in Figure 9. The error between the predicted value of each single model and the true value is different in the prediction effect of each sample point in the test set. It can be seen that different machine learning models have different observation angles on the data space. The machine learning model with high prediction performance cannot achieve better prediction results at every data point, and the model with weak performance can also have small errors at some data points. Therefore, to achieve the optimal performance of the overlay ensemble learning model, it is necessary to analyze the learning ability of each basic learner and the relevance of each learner, build a stacking ensemble learning model, and use the advantages of each single model.