What are the distinctions between Ridge and Lasso?

Question Analysis

The question is asking about the differences between Ridge and Lasso, which are two types of regularization techniques used in linear regression models. Regularization is a method used to prevent overfitting by adding a penalty to the loss function. Understanding how Ridge and Lasso work, and their respective advantages and disadvantages, is essential for a machine learning practitioner to decide which technique to use in a given context.

Answer

Ridge Regression:

• Also Known As: L2 regularization.
• Penalty Term: Adds a penalty equal to the square of the magnitude of coefficients, i.e., ( \lambda \sum_{i=1}^{n} w_i^2 ).
• Effect on Coefficients: Tends to shrink the coefficients of correlated variables towards each other.
• Use Case: When dealing with multicollinearity or when you want to include all predictors in the model.
• Solution: Always provides a solution, as it does not force coefficients to be zero.

Lasso Regression:

• Also Known As: L1 regularization.
• Penalty Term: Adds a penalty equal to the absolute value of the magnitude of coefficients, i.e., ( \lambda \sum_{i=1}^{n} |w_i| ).
• Effect on Coefficients: Can shrink some coefficients to zero, effectively performing variable selection.
• Use Case: When you need a simpler model that can help with feature selection by automatically excluding non-contributing predictors.
• Solution: Can lead to sparse solutions by setting some coefficients exactly to zero.

Key Distinctions:

• Penalty Type: Ridge uses L2 norm, while Lasso uses L1 norm.
• Variable Selection: Lasso can perform variable selection, whereas Ridge cannot.
• Coefficient Shrinkage: Ridge shrinks coefficients evenly, while Lasso can shrink some to zero.

Both techniques help improve the generalization of a model, but the choice between Ridge and Lasso depends on the specific problem requirements, such as the need for feature selection or handling multicollinearity.