Society of Actuaries (SOA) PA Practice Exam

What does it imply when the cross-validation error of a decision tree decreases very slowly?

1. The GLM model might provide a better fit

2. The decision tree is too simple to capture the data

3. The decision tree has sufficient complexity to explain the data

4. The model overfits the training data

The correct answer is: The GLM model might provide a better fit

When the cross-validation error of a decision tree decreases very slowly, it suggests that the decision tree may have sufficient complexity to explain the patterns in the data. As the complexity of a model increases, one would generally expect the model to fit the training data better, which can lead to decreases in cross-validation error. However, if the decrease is slow, this indicates that the model is effectively capturing the underlying structure of the data without being overly complex or simple, suggesting it has enough complexity to explain the data well. In this context, it would not be appropriate to conclude that the generalized linear model (GLM) provides a better fit simply based on the pattern observed with the decision tree. Instead, it highlights the ability of the decision tree to capture the nuances of the dataset. Therefore, the implications drawn from a slowly decreasing cross-validation error point towards a correctly specified model complexity rather than suggesting an alternative model would perform better.