Classic Variable Selection Method by the Creator of Lasso

Lasso (Least Absolute Shrinkage and Selection Operator) regression, proposed by statistician Robert Tibshirani in 1996, represents a classical linear regression regularization technique. Its core principle involves incorporating an L1 regularization term into the loss function to achieve simultaneous variable selection and parameter shrinkage.

The mathematical formulation of Lasso adds a constraint term based on coefficient absolute values to the traditional least squares loss function. This constraint forces certain coefficients to shrink to zero, thereby automatically performing feature selection. Key advantages include handling high-dimensional data, preventing overfitting, and generating interpretable sparse models.

Classical implementation typically involves these critical components: Data standardization: Ensuring features share comparable scales for fair regularization across all coefficients Regularization path computation: Tracking coefficient evolution trajectories by adjusting penalty parameter λ Cross-validation: Automatically selecting optimal λ values to balance bias-variance tradeoff

In extended applications, Lasso has spawned numerous variants such as Elastic Net (combining L1/L2 regularization) and Group Lasso (group variable selection). These methods demonstrate strong performance in high-dimensional data analysis across genomics, economics, and related fields.

Understanding Lasso's variable selection mechanism requires mastery of convex optimization theory and KKT conditions. Implementation algorithms typically employ coordinate descent methods, where this iterative approach proves particularly suitable for handling high-dimensional sparse problems through systematic parameter updates.