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LASSO (Least Absolute Shrinkage and Selection Operator) is a regression analysis method in machine learning that performs both variable selection and regularization to enhance the prediction accuracy and interpretability of the statistical model it produces:

• Objective: LASSO aims to minimize the residual sum of squares (RSS) subject to a constraint on the sum of the absolute values of the model coefficients (the L1 norm). This constraint has the effect of shrinking some coefficients exactly to zero, effectively selecting a simpler model that includes only a subset of the predictors.
  • Mathematical Formulation:
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  where,
• y_i ​ : response variable.
• X _i ​ : predictor variables.
• β: coefficients.
• λ: regularization parameter.

• Regularization Parameter ( 𝜆 λ): This parameter controls the strength of the penalty. When 𝜆 λ is zero, LASSO produces the same coefficients as ordinary least squares (OLS) regression. As 𝜆 λ increases, the impact of the penalty grows, leading to more coefficients being set to zero.

• Advantages:
  • Feature Selection: By forcing some coefficients to be exactly zero, LASSO effectively selects a simpler model that only includes the most important predictors.
  • Improved Interpretability: The resulting model is more interpretable because it includes fewer predictors.
  • Overfitting Reduction: Regularization helps to reduce overfitting, especially when dealing with high-dimensional data.

• Disadvantages:
  • Bias: LASSO introduces bias into the estimates of the coefficients because it shrinks them towards zero.
  • Variable Selection Consistency: LASSO might not always select the correct set of variables, especially if there are highly correlated predictors.

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