The elastic net with α = 1 − ε for some small ε > 0 performs much like the lasso, but removes any degeneracies and wild behavior caused by extreme correlations. More generally, the entire family Pα creates a useful compromise between ridge and lasso. As α increases from 0 to 1, for a given λ the sparsity of the solution to (1) (i.e. the number of coefficients equal to zero) increases monotonically from 0 to the sparsity of the lasso solution.
