Question

isye 6414 elastic net regression simultaneously perform variable selection and shrinkage but cannot select groups of correlated variables

Answer 1

Elastic net regression is a statistical method in Mathematics that performs variable selection and shrinkage. It can select individual variables but may struggle with groups of correlated variables.

Step-by-step explanation:

Elastic net regression is a statistical method that combines the benefits of both ridge regression and lasso regression. It simultaneously performs variable selection and shrinkage by adding a penalizing term to the ordinary least squares equation. The penalty term consists of two parts: the l1-norm penalty which encourages sparsity, and the l2-norm penalty which encourages shrinkage.

While elastic net regression is effective in selecting individual variables, it may have difficulty in selecting groups of correlated variables. This is because the l1-norm penalty tends to select only one variable from a group of highly correlated variables. In such cases, other methods like group lasso or hierarchical clustering can be used.