Financial Risk Manager Part 1

Explanation

Choice B is correct because LASSO regression indeed performs L1 regularization, which adds a penalty equal to the sum of the absolute values of the coefficients to the sum of squared residuals (RSS). This characteristic allows LASSO to perform feature selection by setting some coefficients exactly to zero.

Why other options are incorrect:

• Choice A: Ridge regression does NOT set coefficient estimates to 0. Instead, it shrinks coefficients toward zero but never makes them exactly zero. This is a key distinction between Ridge (L2) and LASSO (L1) regularization.

• Choice C: Elastic net is NOT a hybrid of LASSO and OLS. Rather, it combines both L1 (LASSO) and L2 (Ridge) regularization penalties in a single loss function, providing a balance between the feature selection capability of LASSO and the stability of Ridge.

• Choice D: L2 regularization (Ridge regression) adds a penalty term equal to the sum of the SQUARED values of coefficients (L2 norm), not the absolute values. The absolute value penalty is characteristic of L1 regularization (LASSO).

Key Differences:

• LASSO (L1): Penalty = λ × sum(|coefficients|) - Can set coefficients to zero
• Ridge (L2): Penalty = λ × sum(coefficients²) - Shrinks coefficients but never to zero
• Elastic Net: Combines both L1 and L2 penalties