lasso (least absolute shrinkage and selection operator)

How Does Lasso Work?

Lasso works by minimizing the following objective function:
\[ \text{Minimize} \left( \sum_{i=1}^{n} (y_i - \beta_0 - \sum_{j=1}^{p} \beta_j x_{ij})^2 + \lambda \sum_{j=1}^{p} |\beta_j| \right) \]
Here, \( y_i \) represents the dependent variable, \( x_{ij} \) the independent variables, \( \beta_j \) the coefficients, and \( \lambda \) the tuning parameter that controls the degree of regularization. The larger the value of \( \lambda \), the greater the amount of shrinkage, leading to more coefficients being set to zero.

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