Which statement about the behavior of tree-based methods is true?

Tree-based methods are popular in statistical modeling and machine learning due to their flexibility and effectiveness in both classification and regression tasks. The statement about random forests considering a random subset of predictors at each node accurately reflects a fundamental mechanism of how this ensemble method operates.

In a random forest, each individual tree is constructed by selecting a random sample of the data for training (bootstrap sampling) and, importantly, at each split in the tree, a random subset of the predictors is considered. This randomness helps to ensure that the trees are diverse, which ultimately leads to improved model performance through averaging or voting in the ensemble. By considering only a subset of predictors, random forests reduce the risk of overfitting that can occur with using all predictors for decision trees, thus enhancing the model's ability to generalize to unseen data.

This property is key to the effectiveness of random forests compared to single decision trees, which can be more prone to high variance (the first statement). Bagging, on the other hand, uses multiple trees to form predictions rather than relying on just one, contradicting the second statement. The last statement is false as different tree-based methods, like single trees and ensembles such as bagging and random forests, do not produce identical results; each method