1 pointWhich of the following terms are added for regularization in RIDGERIDGE and LASSOLASSO regression, respectively?

In the context of regression analysis, regularization techniques such as Ridge and Lasso are used to reduce overfitting and improve the model's generalization to new data. Here's a breakdown of the terms added for regularization in each method:

1. Ridge Regression (RIDGE):

   • Ridge regression adds the L2 norm of the coefficients as a penalty term to the loss function. Specifically, the term added is $\lambda \sum_{j=1}^{p} \beta_j^2$, where $\beta_j$ are the coefficients of the model, $p$ is the number of predictors, and $\lambda$ is a tuning parameter that determines the strength of the regularization.

2. Lasso Regression (LASSO):

   • Lasso regression, on the other hand, adds the L1 norm of the coefficients as a penalty term to the loss function. The added term is $\lambda \sum_{j=1}^{p} |\beta_j|$, where $|\beta_j|$ represents the absolute value of the coefficients.

Summary of Regularization Terms:

• Ridge Regression: $L2$ penalty term $\lambda \sum_{j=1}^{p} \beta_j^2$
• Lasso Regression: $L1$ penalty term $\lambda \sum_{j=1}^{p} |\beta_j|$

Thus, Ridge employs L2 regularization, while Lasso uses L1 regularization.