linguistic:paraphrasing, information:classification
Elastic net

Returning to the general case, the fact that the penalty function is now strictly convex means that if x (j) = x (k) {\displaystyle x_{(j)}=x_{(k)}}, β ^ j = β ^ k {\displaystyle {\hat {\beta }}_{j}={\hat {\beta }}_{k}}, which is a change from lasso. In general, if β ^ j β k ^ > 0 {\displaystyle {\hat {\beta }}_{j}{\hat {\beta _{k}}}>0} | β ^ j − β k ^ | ‖ y ‖ ≤ λ 2 − 1 2 (1 − ρ j k), where ρ = X ⊺ X, {\displaystyle {\frac {|{\hat {\beta }}_{j}-{\hat {\beta _{k}}}|}{\|y\|}}\leq \lambda _{2}^{-1}{\sqrt {2(1-\rho _{jk})}},{\text{ where }}\rho =X^{\intercal }X,} is the sample correlation matrix because the x {\displaystyle x} 's are normalized.