When working with regularization, what is the view that illuminates the actual optimization problem and shows why LASSO generally zeros out coefficients?1 pointAnalytical viewGeometric viewProbabilistic viewRegression view
Question
When working with regularization, what is the view that illuminates the actual optimization problem and shows why LASSO generally zeros out coefficients?1 pointAnalytical viewGeometric viewProbabilistic viewRegression view
Solution
The Geometric view illuminates the actual optimization problem and shows why LASSO generally zeros out coefficients. This is because LASSO (Least Absolute Shrinkage and Selection Operator) regularization method imposes a constraint on the sum of the absolute values of the model parameters, the quantity that it minimizes is the sum of the squared residuals plus the sum of the absolute values of the coefficients. This constraint causes some of the parameter estimates to be exactly zero when the tuning parameter lambda is sufficiently large. Hence, LASSO performs both variable selection and regularization. The geometric interpretation of this is that for high dimensions, the probability of the ellipse (which represents the residual sum of squares) hitting the corner (where some coefficients are zero) of the diamond (which represents the L1 penalty) is higher.
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