Society of Actuaries (SOA) PA Practice Exam

How does increasing Lambda affect model parameters?

1. It allows more parameters to contribute

2. It reduces the penalty on complex models

3. It forces more parameters toward zero

4. It enhances model flexibility

The correct answer is: It forces more parameters toward zero

Increasing Lambda in the context of regularization methods, such as Lasso regression, imposes a stronger penalty on the coefficients associated with the model parameters. This means that as Lambda increases, the regularization term becomes more dominant in the loss function. Consequently, many of the model parameters—that contribute to the complexity of the model—are driven towards zero. This encourages simplicity and can help prevent overfitting by effectively limiting the number of parameters that have a significant effect, leading to a more interpretable model subset. The increase in Lambda causes the model to prioritize a lower number of non-zero coefficients, which is beneficial in situations where the dataset has many features, and some of them may not be meaningful. Thus, this effectively shrinks the coefficients of less important features towards zero, resulting in a more parsimonious model. Through this process, the model becomes less flexible, focusing instead on a more robust representation of the underlying data without being overly complex. This characteristic is significant for improving generalization on unseen data. In contrast, the other choices imply different effects that are not representative of the influence of increasing Lambda. For instance, enhancing model flexibility would be more associated with a lower Lambda, allowing more parameters to take on larger values rather than shrinking them.