Final answer:
The rule to stop branching at a threshold is to avoid overfitting and ensure the model finds broad patterns and remains generalizable. Overfitting results in a model capturing noise rather than true data trends, which can lead to poor predictions on new, unseen data.
Step-by-step explanation:
The common rule of thumb to stop branching if a leaf would contain less than 5% of the data points is an effort to avoid overfitting in models. Overfitting occurs when a model becomes too complex, capturing noise rather than the underlying pattern of the data. This can lead to poor generalization to new data.
By limiting the minimum leaf size, we encourage the model to find broader patterns that apply to more data points, rather than fitting to the noise in small, unrepresentative data subsets. Moreover, it is consistent with the principle that having reliable predictions is better than just fitting the training data tightly but failing on new, unseen data.
Additionally, too many branches can lead to complex models that are difficult to interpret and may require more computational resources. This aligns with the scientific emphasis on precision and reliability over crude approximations, a point highlighted by the unreliable nature of heavily rounded numbers. In data analysis, finding an overall pattern and understanding outliers are crucial to drawing accurate conclusions, and this balance is disturbed by overfitting.