LASSOregressio

LASSO regression, which stands for Least Absolute Shrinkage and Selection Operator, is a type of linear regression analysis that performs L1 regularization. This technique is commonly used in statistical modeling and machine learning for its ability to perform variable selection and prevent overfitting. The core idea behind LASSO is to add a penalty term to the standard linear regression cost function. This penalty is proportional to the absolute value of the magnitude of the coefficients. Mathematically, the LASSO objective function is the sum of the residual sum of squares and the absolute value of the coefficients multiplied by a tuning parameter, lambda.

The key characteristic of LASSO regression is that the L1 penalty can force some coefficients to become exactly zero. This is unlike Ridge regression, which uses an L2 penalty and shrinks coefficients towards zero but rarely makes them exactly zero. When a coefficient is zeroed out, the corresponding predictor variable is effectively removed from the model, thus performing automatic feature selection. This is particularly useful when dealing with datasets that have a large number of predictor variables, many of which may be irrelevant or redundant. The tuning parameter, lambda, controls the strength of the penalty. A larger lambda leads to more coefficients being shrunk to zero, resulting in a sparser model.

LASSO regression is beneficial in situations where interpretability is important, as it simplifies the model by removing less important features. It can also improve the predictive accuracy of models by reducing variance, especially when the number of features is large relative to the number of observations. The selection of the optimal value for lambda is typically done using cross-validation.