What hyperparameter determines how deep a decision tree can grow?

The hyperparameter that determines how deep a decision tree can grow is indeed max_depth. This parameter sets a limit on the number of levels in the tree, which directly influences its depth. By specifying a maximum depth, you can prevent the decision tree from becoming overly complex and overfitting to the training data.

Limiting the depth of the tree is critical in managing the model's complexity and ensuring that it generalizes well when applied to unseen data. A deeper tree might capture more detailed patterns in the training set, but can also lead to a model that performs poorly on new data due to its increased tendency to memorize rather than learn generalizable patterns.

The other hyperparameters play different roles in tree construction. For instance, min_samples_leaf dictates the minimum number of samples that a leaf node must contain, while min_samples_split regulates the minimum number of samples required to split an internal node. The splitter refers to the strategy used to choose the feature and threshold for splitting nodes but does not directly control the tree's depth.

Understanding these parameters is crucial for effectively tuning a decision tree algorithm, as they directly impact model performance and complexity.