Explain the contrast between L1 and L2 regularization methods used in regression analysis, and when one would be favored over the other.

Question Analysis

This question is asking you to explain the differences between L1 and L2 regularization methods, which are techniques used to prevent overfitting in regression models by penalizing large coefficients. The question also requires you to discuss scenarios where one method might be preferred over the other. This is a technical question assessing your understanding of machine learning techniques, specifically regularization in regression analysis.

Answer

L1 Regularization (Lasso Regression):

• Penalty: Adds an L1 penalty equal to the absolute value of the magnitude of coefficients.
• Feature Selection: Encourages sparsity in the model, meaning it tends to reduce some coefficients to zero, effectively performing feature selection.
• When to Use:
  • When you have many features and suspect that only a few are significant.
  • When you desire a simpler, more interpretable model with fewer features.

L2 Regularization (Ridge Regression):

• Penalty: Adds an L2 penalty equal to the square of the magnitude of coefficients.
• Feature Shrinkage: Tends to shrink coefficients evenly, rarely reducing them to exactly zero.
• When to Use:
  • When multicollinearity is present, as it can help stabilize the estimates.
  • When you want to retain all the features but prevent overfitting by reducing the impact of less important features.

Comparison and Preference:

• L1 vs. L2: L1 regularization is preferred when feature selection is important, whereas L2 is useful when you want to retain all features but control overfitting.
• Hybrid Approach: Elastic Net combines both L1 and L2 penalties, which can be useful when there are multiple correlated features.

In summary, the choice between L1 and L2 regularization depends on your specific needs regarding model complexity and feature selection.