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This lecture covers a diverse set of regularization approaches, including the L0 quasi-norm and the Lasso method. It discusses best subset selection, the trade-off between fitting and the number of variables, and the NP-hardness of the problem. The Lasso, or Least Absolute Shrinkage and Selection Operator, is introduced as a convex but non-differentiable optimization problem with efficient algorithms for solution. The lecture also explores the extension to quasi-norms and the difference between constrained and regularized Lasso regression problems.