Society of Actuaries (SOA) PA Practice Exam

How does Elastic Net Regression perform feature selection?

1. By only including a single predictor variable

2. By adding a penalty to the loglikelihood based on the coefficients

3. By selecting features solely based on statistical significance

4. By exclusively applying LASSO regression techniques

The correct answer is: By adding a penalty to the loglikelihood based on the coefficients

Elastic Net Regression performs feature selection by adding a penalty to the loglikelihood based on the coefficients. This penalty combines both L1 and L2 regularization techniques, which means it incorporates elements of both LASSO (which applies L1 regularization) and Ridge (which applies L2 regularization). With the L1 penalty, some coefficients can be shrunk to zero, effectively removing certain features from the model; this aspect of LASSO helps in feature selection. The L2 penalty, on the other hand, helps to stabilize the selection process by minimizing overfitting. By leveraging this dual-penalty approach, Elastic Net can manage situations where the number of predictors exceeds the number of observations or when predictors are highly correlated. This capability not only improves model performance but also aids in identifying a more interpretable model containing relevant features. The other options do not accurately reflect the behavior of Elastic Net. It does not restrict itself to a single predictor variable, nor does it focus solely on statistical significance for feature selection. While it uses LASSO techniques as part of its methodology, it is not limited to them exclusively because it incorporates Ridge regression features as well. This hybrid approach is what distinguishes Elastic Net in feature selection, allowing it to