Which statements are true regarding random forests?

The statement that the trees are decorrelated is true and reflects a key characteristic of random forests. In the context of ensemble learning, specifically forest-based methods like random forests, individual trees are constructed from different subsets of the data and use a subset of the predictors available for splitting at each node. This process—often referred to as bagging (bootstrap aggregating)—ensures that the trees are not correlated with each other, which is essential for minimizing overfitting and increasing the robustness of the model.

The decorrelation of trees enhances the performance of the model as it leverages the diversity among the trees to improve the overall prediction accuracy. By aggregating predictions from multiple independent trees—each capturing different aspects of the data—random forests can achieve better entropy and variance reduction compared to a single decision tree.

Other statements do not accurately describe the characteristics of random forests. While splits occur at various nodes in each tree, it's not true that all predictors are utilized at each split, or that all trees require the same predictors. In fact, one of the strengths of random forests is their ability to create varying tree structures, making them versatile and powerful in handling complex datasets.