Lasso Regression - Variable Selection and Regularization Technique

Lasso regression is a statistical technique widely used in data analysis to create parsimonious and interpretable models. As a variant of linear regression, it performs simultaneous variable selection and regularization by incorporating an L1 penalty term into the ordinary least squares (OLS) objective function. This penalty term effectively shrinks the coefficients of less significant variables to zero, enabling identification of the most relevant features in datasets. In Python implementations using scikit-learn, lasso regression can be applied through the Lasso class, where the key parameter 'alpha' controls the regularization strength. The algorithm solves the optimization problem: minimize ||y - Xw||²₂ + α * ||w||₁, where ||w||₁ represents the L1 norm of coefficients. This approach is particularly valuable when dealing with high-dimensional data, as it automatically performs feature selection while maintaining model interpretability. Lasso regression's practical applications span multiple fields including economics, social sciences, and engineering, where it serves as an effective tool for processing statistical data and building robust predictive models. The method's ability to handle multicollinearity and produce sparse solutions makes it superior to traditional regression techniques in many real-world scenarios.