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What is the type of regularization inherent in the LASSO case?
Group of answer choices: L1, L2, No Regularization, L1+L2

Answer :

The type of regularization inherent in the LASSO (Least Absolute Shrinkage and Selection Operator) case is L1 regularization. Let me explain further.

Regularization is a technique used in linear regression models to prevent overfitting by adding a penalty to the loss function used to train the model. The idea is to discourage complex models to improve generalization and performance on new, unseen data.

In the LASSO method, the L1 norm of the coefficient vector is added as a penalty term to the linear regression loss function. This penalty is expressed mathematically as:
[tex]\text{Loss} = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 + \lambda \sum_{j=1}^{p} |\beta_j|[/tex]
where:

  1. [tex]y_i[/tex] represents the actual target value.

  2. [tex]\hat{y}_i[/tex] represents the predicted target value.

  3. [tex]|\beta_j|[/tex] is the absolute value of the coefficients of the features.

  4. [tex]\lambda[/tex] is a tuning parameter that controls the strength of the regularization.

The L1 penalty term [tex]\lambda \sum_{j=1}^{p} |\beta_j|[/tex] encourages the shrinkage of some coefficients to exactly zero, effectively performing feature selection. This means that LASSO can not only help in reducing overfitting but also in identifying a subset of features that are most predictive of the output.

Therefore, the correct choice from the given options is L1 regularization.

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