L1 Regularization: Sparse Solutions and Dimensionality Reduction

This lecture covers L1 regularization, focusing on the concept of replacing empirical risk with a regularized version. It explores how L1 regularization leads to sparse solutions by relying on a few significant entries from the observation vector. The lecture also discusses the concept of dimensionality reduction and the benefits of using elastic-net regularization. Various mathematical derivations and interpretations related to Laplacian priors and optimization problems are presented.