6. L1 & L2 Regularization

We introduce "regularization", our main defense against overfitting. We discuss the equivalence of the penalization and constraint forms of regularization (see Hwk 4 Problem 8 for a precise statement). We compare regularization paths of L1- and L2-regularized linear least squares regression (i.e. "lasso" and "ridge" regression, respectively), and give a geometric argument for why lasso often gives "sparse" solutions. Finally, we present "coordinate descent", our second major approach to optimization. When applied to the lasso objective function, coordinate descent takes a particularly clean form and is known as the "shooting algorithm"
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