/ˈlæs.oʊ rɪˈɡrɛʃ.ən/
noun … “OLS with selective pruning.”
Lasso Regression is a regularization technique for Linear Regression that extends Ordinary Least Squares by adding a penalty proportional to the absolute values of the coefficients. This encourages sparsity, effectively shrinking some coefficients to exactly zero, performing variable selection alongside estimation. Lasso is particularly useful in high-dimensional datasets with many predictors, where identifying the most relevant features improves interpretability and predictive performance while controlling overfitting.
Mathematically, Lasso minimizes the objective function:
β̂ = argmin ||Y - Xβ||² + λ Σ |βⱼ|Here, Y is the response vector, X the predictor matrix, β the coefficient vector, and λ ≥ 0 the regularization parameter controlling the strength of shrinkage. Unlike Ridge Regression, which penalizes squared magnitudes and shrinks coefficients continuously, the L1 penalty of Lasso allows coefficients to reach exactly zero, automatically selecting features.
Lasso Regression connects with key statistical concepts such as Covariance Matrix analysis, Expectation Values, and residual Variance assessment. It is widely applied in genomics, text analytics, finance, and machine learning pipelines where interpretability and dimensionality reduction are essential. Lasso also serves as a foundation for Elastic Net, which combines L1 and L2 penalties to balance sparsity and coefficient stability.
Example conceptual workflow for Lasso Regression:
collect dataset with predictors and response
standardize predictors for comparable scaling
select a range of λ values to control regularization
fit Lasso Regression for each λ
evaluate performance via cross-validation
choose λ that balances prediction accuracy and sparsity
interpret selected features and coefficient magnitudesIntuitively, Lasso Regression is like a gardener trimming a dense hedge: it prunes insignificant branches (coefficients) entirely while letting the strongest grow, resulting in a clean, interpretable structure. This selective pruning transforms complex, high-dimensional data into a concise, actionable model.