In what circumstances would you apply Ridge or Lasso regression, and how would you determine which to use?

Question Analysis

The question asks about the application contexts of two regularization techniques in linear regression: Ridge and Lasso regression. The candidate needs to understand the purpose of these techniques, which is to prevent overfitting by adding a penalty to the loss function. The question also requires an explanation of the criteria used to choose between Ridge and Lasso regression.

Answer

Ridge and Lasso Regression are both regularization techniques used to handle multicollinearity and prevent overfitting in linear regression models by adding a penalty term to the loss function.

Ridge Regression (L2 regularization):

• Use Cases:
  • When you have a large number of features, and you suspect some of them are collinear.
  • When you want to shrink the coefficients of less important features but not eliminate them entirely.
• Penalty Term: Adds the squared magnitude of coefficients as a penalty term.
• Effect: Tends to distribute the coefficient weights more evenly across all features.

Lasso Regression (L1 regularization):

• Use Cases:
  • When you suspect that only a subset of the features are actually useful for predicting the target.
  • When you want to perform feature selection by automatically driving some feature coefficients to zero.
• Penalty Term: Adds the absolute value of the magnitude of coefficients as a penalty term.
• Effect: Can shrink some coefficients to exactly zero, effectively performing variable selection.

Determining Which to Use:

• Feature Selection: If feature selection is important, Lasso is often more appropriate since it can zero out coefficients of less important features.
• Model Interpretability: If you need a more interpretable model with fewer variables, Lasso might be preferred.
• Predictive Accuracy: If all features are believed to be potentially useful and collinearity is a concern, Ridge can be a better choice.
• Cross-Validation: Use cross-validation to empirically determine which model performs better on your specific dataset.

By understanding these distinctions, you can choose the appropriate regularization method based on the specific needs and characteristics of your dataset.