What does the selection of √p features at each split help to achieve in a random forest?

The selection of √p features at each split in a random forest is fundamentally aimed at reducing multicollinearity among features. In a random forest, when constructing decision trees, using a subset of features (specifically √p, where p is the total number of features) helps to ensure that each individual tree in the ensemble is not overly influenced by highly correlated features. This randomization introduces diversity among the trees, allowing the model to capture different patterns in the data and reduces the risk of overfitting to a specific set of features.

By limiting the number of features considered for each split, the random forest can create different paths and splits in different trees, which mitigates the dominance of any single feature due to multicollinearity. This is important for ensuring that the model remains robust and generalizes well to unseen data, instead of being swayed by correlated features that could skew the results. Overall, this approach promotes a more stable and interpretable model.