Society of Actuaries (SOA) PA Practice Exam

In LASSO, what happens to some coefficients during the dimensionality reduction process?

1. They are all set to one

2. Some coefficients are floated to infinity

3. Some coefficients are coerced to zero

4. All coefficients are preserved

The correct answer is: Some coefficients are coerced to zero

LASSO, which stands for Least Absolute Shrinkage and Selection Operator, is a regression analysis method that performs both variable selection and regularization to enhance the prediction accuracy and interpretability of the statistical model it produces. The key feature of LASSO is its ability to shrink some of the coefficients towards zero, effectively carrying out dimensionality reduction. When the LASSO penalty, which involves the absolute values of the coefficients, is applied, some coefficients are driven to exactly zero. This occurs because LASSO imposes a constraint on the size of the coefficients, leading to a situation where some variables may contribute little to the predictive power of the model. By setting these coefficients to zero, LASSO effectively excludes those variables from the model, which simplifies it and mitigates overfitting. This process not only aids in creating a more interpretable model but also emphasizes the most significant variables that impact the outcome. The coefficients that are not zero represent the most important predictors in the context of the data being modeled, allowing for clearer insights into relationships within the dataset. In summary, during the LASSO dimensionality reduction process, the coefficients of less impactful variables are coerced to zero, enabling a streamlined and more meaningful model without sacrificing