# Predicting Putting Development Using Machine Learning Methods Based on RIOCHTrack Data
## 3 Results and Discussion  
### Hyperparameters Selection  
Because different hyperparameters may have different effects on the model, the grid search method was adopted to optimize the parameters, and the optimal parameters of the model were screened through cross-validation. The dataset will be divided, with 80% of the data allocated as the training set and the remaining 20% designated as the testing set. It should be emphasized that grid search with cross-validation was performed on the training datasets. Cross-validation [33] randomly divides the training dataset into K parts. K-1 of these subsets are then used for model training, and the remaining datasets are used for evaluation. This process is repeated K times, with each subset acting as the evaluation set once. Finally, the average value of the K test results is determined. For each model, we selected the set of hyperparameters resulting in the highest R\({}^{2}\) as the optimal value. Consequently, model overfitting can be effectively suppressed and the optimal parameters obtained. This article adopts a 5-fold cross-validation to search for hyperparameters, the process is shown in Figure 7. The mean R\({}^{2}\) based on a 5-fold cross-validation was used to evaluate the performance of a model. Regarding the selection of hyperparameters in SVR, the kernel function and other parameters can be crucial. ALL the hyperparameters were obtained through 5-fold cross-validation. The form of the kernel function determines the properties of the feature space. Also, different kernel functions correspond to different hyperparameters. The penalty parameter C serves to establish the model's tolerance for misjudging the target. A higher value of C indicates a lower tolerance for misclassification, resulting in a larger loss function. Epsilon determines the model's tolerance for errors and controls the smoothness of the regression curve. In general, the larger the epsilon, the higher the smoothness of the model, but the lower the accuracy of the model. The selection of kernel parameters directly governs the model's fitting ability. With a larger \(\gamma\), the model becomes more complex and is at a higher risk of overfitting. Random Forest, GBDT, and Extra Trees are ensemble methods. Ensemble learning is the process of combining several weak learners into one strong learner to improve the performance of a model. The number of estimators (or trees) is a crucial hyperparameter that impacts the accuracy of a model's predictions. Increasing the maximum number of levels allows the model to gain more information about the data. The number of trees determines the running time of the model. The higher the number of trees, the more times the model needs to be trained. Ensemble learning models are based on decision  
Figure 7: Process of 5-fold cross-validation. trees. Max_depth, min_samples_leaf, and min_samples_split are important parameters of a decision tree. The max_depth determines the fitting ability and complexity of the model. An excessive tree depth tends to cause model overfitting_min_samples_leaf represents the minimum number of samples required to construct a decision leaf node. When the number of samples within the node is less than this threshold, pruning operations will be performed. The minimum number of samples required for internal node redistribution (min_samples_split) limits the conditions for the subtree to continue partitioning. The smaller the value, the more refined the model, and the longer the training time. In addition, the learning rate is also important for GBDT, which determines the size of the gradient descent step for each iteration, and a too-high learning rate may cause the model to fail to converge, which determines the rate at which the model reduces the loss function. Too high a learning rate may prevent model convergence. ANN utilizes many hyperparameters [34], including the number of hidden layers, the number of neurons in each layer, and iterations as well as the activation function and learning rate.