I've coded an adaptive lasso based on Zou 2006 and I'm in the process of figuring out how to implement the adaptive elastic net. The L1 penalization has associated weights $w_j$, proportional to the marginal regression coefficients $\hat {\beta_j}$. Since we're doing a grid search for all the values of $\lambda_1$ in the range of $[0,\lambda_{1 max}]$, where the latter value shrinks all of the estimated coefficients to 0, $\lambda_{1 max}$ has to take into account weights $w_j$
However, $\lambda_2$ for the $L_2$ penalty is supposed to be unaffected by weights $w_j$. The value of $\lambda_{1 max}$ depends on weights
dotp = abs(X0' * (Y - predictedMu)).*LambdaWeights.^-1;
lambdaMax = max(dotp) / (N*alpha);
Where LambdaWeights is the set of weights $w_j$. I calculate the threshold using the same set of weights. NOW, given that I define the per predictor penalty using in the threshold, I think I don't have to modify $\lambda_1$ or $\lambda_2$. Am I correct in thinking this?
