Society of Actuaries (SOA) PA Practice Exam

What is the role of hyperparameters in regression methods like Lasso and Ridge?

1. To eliminate all predictor variables

2. To control the extent of coefficient reduction

3. To increase model complexity

4. To ensure all variables are included

The correct answer is: To control the extent of coefficient reduction

In regression methods such as Lasso and Ridge, hyperparameters play a crucial role in managing the regularization process, which aims to prevent overfitting by controlling the size of the coefficients in the model. The hyperparameters specifically guide the extent to which the coefficients of the predictor variables are shrunk toward zero. In Lasso regression, the hyperparameter determines the degree of penalty applied to the absolute size of the coefficients, which can lead to some coefficients being reduced to exactly zero. This effectively performs variable selection, allowing the model to focus on the most significant predictors. In Ridge regression, the hyperparameter controls the penalty applied to the sum of the squares of the coefficients, allowing them to be minimized but not necessarily brought to zero. This helps maintain all predictor variables in the model while reducing their influence, hence controlling multicollinearity. The correct option highlights that the essence of using hyperparameters is to manage the regularization effect and, as such, adjust how strongly the coefficients are reduced, ensuring that the model achieves a balance between bias and variance. This action leads to improved model performance on new, unseen data.