Society of Actuaries (SOA) PA Practice Exam

How are Boosted Trees constructed?

1. By using a single tree to evaluate all data points.

2. By adding trees sequentially to fit the residuals from prior trees.

3. All trees are built simultaneously with one another.

4. By relying only on the original data without revisions.

The correct answer is: By adding trees sequentially to fit the residuals from prior trees.

Boosted Trees are constructed by adding trees sequentially to fit the residuals from prior trees. This process is known as boosting, where each new tree aims to correct the errors made by the existing ensemble of trees. In each iteration, the algorithm typically takes the predictions from all previous trees and computes the residuals, which represent the difference between the actual outcomes and the predictions. The new tree is then added to minimize these residuals, improving the overall prediction accuracy of the model. This sequential approach allows Boosted Trees to build a strong predictive model from a collection of weak learners (individual trees), as each tree focuses on the mistakes of the previous ones. This is in contrast to strategies where models are constructed independently or simultaneously, which do not leverage the learning from earlier iterations in the same way boosting does.