Society of Actuaries (SOA) PA Practice Exam

Why is regularization used in statistical modeling?

1. To increase the flexibility of the model

2. To reduce noise by increasing the model's variance

3. To add a penalty term that limits the impact of coefficients

4. To ensure that coefficients are unaffected by lambda value

The correct answer is: To add a penalty term that limits the impact of coefficients

Regularization is a technique used in statistical modeling to prevent overfitting while maintaining a model's predictive power. The correct answer highlights how regularization works by adding a penalty term to the loss function. This penalty discourages overly large coefficients in the model. By limiting the impact of individual coefficients, regularization helps to stabilize the model, making it less sensitive to the fluctuations and noise in the training data. This balancing act is crucial because while a flexible model may fit the training data closely, it can also capture irregular patterns that do not generalize well to unseen data. The penalty term introduced by regularization techniques, such as Lasso (which uses L1 regularization) or Ridge (which uses L2 regularization), is a strategic tool to enforce this control over the coefficients, leading to more robust model performance in practice. In contrast, other options do not accurately identify the primary purpose of regularization. Increasing model flexibility or reducing noise by increasing variance diverges from the fundamental goal, which is to promote a more generalizable fit. Additionally, the statement about coefficients being unaffected by the lambda value is misleading; in fact, the lambda value is essential in regulating how much penalty is imposed, thereby directly influencing the coefficients. Thus, recognizing