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

Answer :

The type of regularization inherent in the LASSO case is L1 regularization, also known as L1 norm or L1 penalty.

LASSO stands for 'Least Absolute Shrinkage and Selection Operator.' It is a regression analysis method that aims to enhance the prediction accuracy and interpretability of the statistical model it produces.

Here's a step-by-step explanation of why LASSO uses L1 regularization:

  1. Objective of LASSO:
    LASSO is used in linear regression to prevent overfitting and to select a simpler model by performing both variable selection and regularization.

  2. Mathematical formulation:
    The LASSO optimization problem can be expressed as:
    [tex]\min \left( \sum_{i=1}^{n} (y_i - \beta_0 - \sum_{j=1}^{p} \beta_j x_{ij})^2 + \lambda \sum_{j=1}^{p} |\beta_j| \right)[/tex]
    Here, the term [tex]\sum_{j=1}^{p} |\beta_j|[/tex] is the L1 norm of the coefficients, and [tex]\lambda[/tex] is a tuning parameter that controls the strength of regularization.

  3. Regularization through the L1 norm:
    L1 regularization introduces a penalty equal to the absolute value of the magnitude of the coefficients. The effect is twofold:

    • Shrinkage: Larger coefficients are penalized more, which typically leads to smaller coefficients.
    • Sparsity: By increasing [tex]\lambda[/tex], many coefficients can become exactly zero, hence selecting only a subset of features, making the model easier to interpret.

  4. Comparison with L2 Regularization (Ridge):
    Unlike LASSO, Ridge regression uses L2 regularization, which penalizes the square of the coefficients' magnitudes and tends to shrink coefficients towards zero but not exactly to zero.

Therefore, the correct choice for the LASSO regularization type is L1.

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