Free CAS MAS-II (Modern Actuarial Statistics II) Statistical Learning Practice Questions
Statistical learning on CAS Exam MAS-II covers K-nearest neighbors, decision tree pruning and ensemble methods (random forests, boosting), principal components analysis, K-means and hierarchical clustering, neural network output interpretation, and predictive-accuracy measures (lift, Gini, AUROC, double lift chart) for P&C ratemaking and classification (CAS).
Sample Questions
Question 1
Easy
Which of the following best distinguishes K-means clustering from agglomerative hierarchical clustering?
Solution
A is correct. K-means partitions observations into a pre-specified number of disjoint clusters by iteratively reassigning observations and updating centroids; the analyst must choose K before running the algorithm. Agglomerative hierarchical clustering instead builds a tree of nested partitions by successively merging the closest groups, and any desired number of clusters can be obtained after the fact by cutting the dendrogram at an appropriate height. This is the defining structural contrast between the two methods.
Question 2
Medium
Compared with bagging, random forests are MOST LIKELY to improve out-of-sample predictive accuracy primarily because they...
Solution
B is correct. Bagging averages predictions from trees fit to bootstrap samples, which by itself only modestly reduces variance because the trees remain highly correlated. The trees tend to share top-level splits on the same dominant predictors. Random forests restrict each split to a random subset of predictors, which forces the trees to diverge and lowers the pairwise correlation between them. Because the variance of an average of correlated predictors depends on that correlation, the decorrelation step lowers ensemble variance below what bagging achieves.
Question 3
Hard
An actuary is comparing a candidate GLM rating plan against the insurer's current rating plan on the same set of holdout policies, with the goal of demonstrating that the candidate plan more accurately segments risk than the incumbent. Which of the following evaluation tools is MOST APPROPRIATE for that specific comparison?
Solution
A is correct. A double lift chart is purpose-built to compare two competing rating plans on the same exposure base. Policies are sorted by the ratio of candidate-to-incumbent predicted premiums and grouped into buckets, and actual loss ratios within each bucket reveal whether the candidate plan identifies pricing dislocations that the incumbent missed. The other tools either evaluate a single model in isolation, rely on an in-sample fit that is optimistic, or recast a continuous-outcome rating problem as a binary classification problem and discard the loss-cost signal that the comparison should hinge on.