$defl{|!|}$
Given the elastic net regression
$$min_b frac{1}{2}l y – Xb l^2 + alphalambda l bl_2^2 + (1 – alpha) lambda l bl_1$$
how can an appropriate range of $lambda$ be chosen for cross-validation?
In the $alpha=1$ case (ridge regression) the formula
$$textrm{dof} = sum_j frac{s_j^2}{s_j^2+lambda}$$
can be used to give an equivalent degrees of freedom for each lambda (where $s_j$ are the singular values of $X$), and degrees of freedom can be chosen in a sensible range.
In the $alpha=0$ case (lasso) we know that
$$lambda > lambda_{textrm{max}} = max_j|sum_t y_t X_{tj}|$$
will result in all $b_j$ being zero, and $lambda$ can be chosen in some range $(0, lambda_textrm{max})$.
But how to handle the mixed case?