Lasso Regression

Lasso Regression

Lasso Regression, which stands for Least Absolute Shrinkage and Selection Operator, is a type of linear regression that incorporates regularization to enhance prediction accuracy and interpretability in statistical models. It is particularly useful when dealing with datasets that have many features or variables.

The primary objective of Lasso Regression is to minimize the loss function of the linear model while also imposing a penalty on the absolute size of the coefficients. This penalty term, known as L1 regularization, encourages the model to shrink some coefficients to zero, effectively performing variable selection. This means that Lasso Regression can help identify the most significant predictors in a dataset and discard irrelevant or less impactful features.

Mathematically, Lasso Regression solves the following optimization problem:

minimize ||y - Xβ||² + λ||β||₁

Here, y represents the target variable, X is the feature matrix, β denotes the coefficient vector, ||y - Xβ||² is the residual sum of squares, and λ is the regularization parameter that controls the strength of the penalty. A larger value of λ results in more coefficients being shrunk towards zero, which can help reduce overfitting but may also lead to underfitting if set too high.

Lasso Regression is widely used in fields such as finance, biology, and machine learning for its ability to simplify models and improve prediction accuracy. It is particularly effective in high-dimensional datasets where the number of predictors exceeds the number of observations.