# Hybrid Modeling for Stream Flow Estimation: Integrating Machine Learning and Federated Learning
## 3 Material and Experimental Methods
### Extra Trees  
ETs, also known as extremely randomized trees, is a machine learning model that belongs to the ensemble learning family, similar to the RF algorithm. It is particularly useful for both classification and regression tasks. The main distinction between the ETs model and a traditional RF lies in the way decision-making is performed at each node in the tree. In an RF, the decision at each node is based on a subset of features randomly selected from the available set of features, and the majority vote from these trees determines the final classification decision. In contrast, ETs take a more random approach. Not only do they select random subsets of features for each node, but they also choose random cut points to divide the data at each node. This randomization introduces additional diversity and variability among the individual trees in the ensemble.  
Figure 6: The general structure of the RF classifier (RFC) model in this research.  
Another key difference is that ETs use the entire original sample as input during the training process, whereas RF typically uses bootstrapped samples (i.e., random samples with replacement) for each tree. By incorporating these sources of randomness, ETs aim to reduce the variance in the model, making them less susceptible to overfitting and enhancing their generalization capabilities. This property is especially valuable when working with high-dimensional data or noisy datasets. During the classification phase, the ETs model aggregates the predictions from all the individual trees and determines the final classification decision based on the majority vote among the trees. This democratic voting process helps to ensure robust and accurate predictions. Due to their robustness, simplicity, and ability to handle high-dimensional datasets, ETs have found widespread applications in various fields, including computer vision, bioinformatics, and finance [66; 67]. The randomization techniques employed by ETs contribute to their effectiveness as a powerful and flexible machine learning algorithm.  
Figure 7 depicts the structure of the ETs model applied to the river flow data in this research. As an extension of the RF algorithm, the ETs model, also known as extremely randomized trees, exhibits distinct characteristics in its construction and decision-making process. Figure 7 exemplifies the unique structure of the ETs model, highlighting its randomization techniques and ensemble learning principles. By incorporating these distinct characteristics, the ETs model proves to be a powerful and effective algorithm for handling river flow data and other complex datasets.  
Figure 7 in the research paper illustrates the structure and functionality of ETs when applied to river flow data. ETs, or extremely randomized trees, are highlighted for their unique construction and decision-making processes. The figure showcases the ensemble of individual trees and emphasizes the randomization techniques employed in their creation. This visual representation helps convey how ETs use the entire original sample during training, offering robustness against overfitting and enhancing generalization capabilities. As a powerful and flexible machine learning algorithm, ETs have found widespread applications in various fields, including computer vision, bioinformatics, and finance. In the context of river flow data analysis, Figure 7 serves as a valuable visual aid, making complex concepts more accessible and enhancing the research's overall clarity and impact.