What are the distinctions between Ridge and Lasso?

Question Analysis

The question is asking about the differences between two regularization techniques used in linear regression models: Ridge and Lasso. This is a technical question that assesses your understanding of how these methods work and how they impact the model. Regularization is a technique used to prevent overfitting by adding a penalty to the loss function, and both Ridge and Lasso are popular methods for this purpose. It is important to explain the mathematical differences, their effects, and when each method might be preferred.

Answer

Ridge Regression:

• Also Known As: L2 Regularization
• Penalty Term: Ridge adds a penalty equal to the square of the magnitude of coefficients. The penalty term (\lambda \sum_{i=1}^{n} \beta_i^2) is added to the loss function, where (\lambda) is the regularization parameter.
• Effect on Coefficients: Ridge regression tends to shrink the coefficients of correlated features towards each other, but never to zero.
• Use Case: Ridge is preferred when there are many small/medium-sized effects and multicollinearity is present.

Lasso Regression:

• Also Known As: L1 Regularization
• Penalty Term: Lasso adds a penalty equal to the absolute value of the magnitude of coefficients. The penalty term (\lambda \sum_{i=1}^{n} |\beta_i|) is added to the loss function.
• Effect on Coefficients: Lasso can shrink some coefficients to exactly zero, effectively performing variable selection.
• Use Case: Lasso is useful when we want to reduce the number of predictors, as it can automatically select a simpler model that includes only a subset of features.

Key Distinctions:

• Coefficient Shrinkage: Ridge shrinks coefficients evenly, while Lasso can eliminate some coefficients entirely.
• Model Complexity/Simplicity: Lasso can produce simpler models by selecting a subset of features.
• Handling Multicollinearity: Ridge is more suitable for datasets with multicollinearity.

In summary, the choice between Ridge and Lasso depends on the specific needs of the problem, such as the importance of feature selection or the presence of multicollinearity.