Lasso and Regularized Regression

Lasso and Regularized Regression. Penalized estimators, oracle inequalities, and elastic net.

Foundations and canonical references

The standard treatments of lasso and regularized regression approach the subject from complementary angles. Hastie, Statistical Learning with Sparsity: The Lasso and Generalizations (2015) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to.

Supporting and adjacent work

A number of supporting contributions sharpen specific aspects of lasso and regularized regression or connect it to neighbouring problems. Regression Shrinkage and Selection via the Lasso (Tibshirani, 1996) contributes to this area as one of the supporting references that inform current practice.

Open methodological questions for lasso and regularized regression include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.