What is the typical choice for the number of features selected at each split in a random forest model?

In a random forest model, the typical choice for the number of features selected at each split is the square root of the total number of features, denoted as √p. This approach is based on the principle of reducing the correlation among the trees in the forest, thereby enhancing their diversity and overall predictive power.

When using the square root of the number of features, each tree is trained on a different subset of features, which helps to create a robust ensemble. This method strikes a balance: selecting too few features might lead to suboptimal splits, while selecting too many could result in highly correlated trees that do not improve the model's performance much.

This choice is particularly beneficial in high-dimensional datasets commonly found in practice, allowing the model to maintain interpretability while still capturing the underlying patterns in the data effectively. By considering a smaller, randomized sample of features, random forests also capitalize on the "wisdom of crowds," where multiple, less correlated models combine to produce a more accurate overall prediction.