What are the distinctions between Ridge and Lasso?

Question Analysis

The question is asking about the differences between Ridge and Lasso regression techniques, which are both used to prevent overfitting in machine learning models. Understanding the distinctions between these two methods is important for selecting the appropriate technique based on the specific characteristics and needs of the dataset you are working with. This question tests your knowledge of regularization techniques in linear regression, their mathematical foundations, and their practical implications.

Answer

Ridge and Lasso are both regularization techniques used to enhance the generalization performance of linear regression models by adding a penalty term to the loss function. Here are the key distinctions between them:

• Penalty Type:

  • Ridge (L2 Regularization): Adds a penalty equal to the square of the magnitude of coefficients (i.e., (\lambda \sum \beta_i^2)). This penalty term discourages large coefficients but does not enforce zero coefficients.
  • Lasso (L1 Regularization): Adds a penalty equal to the absolute value of the magnitude of coefficients (i.e., (\lambda \sum |\beta_i|)). This can shrink some coefficients to exactly zero, effectively performing feature selection.

• Resulting Coefficients:

  • Ridge: Tends to produce models with all features having non-zero coefficients, resulting in a more distributed impact across all features.
  • Lasso: Can result in sparse models where some feature coefficients are exactly zero, which is useful for feature selection.

• Use Cases:

  • Ridge: Preferable when you have many small/medium-sized effects spread across all predictors, and you want to retain all features in the model.
  • Lasso: Suitable when you expect that only a small number of predictors are important, and you want to perform variable selection.

• Complexity:

  • Ridge: Generally easier to compute as it involves solving a system of linear equations.
  • Lasso: Can be more complex to compute due to the non-differentiability at zero, requiring specialized optimization techniques like coordinate descent.

Understanding these distinctions will help you choose the right regularization technique based on the nature of your data and the goals of your analysis.