How could one tune the parameter alpha of the sparse group lasso method (SGL) based on cross-validation?

The sparse-group lasso (SGL) method presented by Simon et al. as follow :

$$\min _{\beta} \frac{1}{2 n}\left\|y-\sum_{l=1}^{m} X^{(l)} \beta^{(l)}\right\|_{2}^{2}+(1-\alpha) \lambda \sum_{l=1}^{m} \sqrt{p_{l}}\left\|\beta^{(l)}\right\|_{2}+\alpha \lambda\|\beta\|_{1}$$

where $$\alpha \in[0,1]-$$ a convex combination of the lasso and group lasso penalties $$(\alpha=0 \text { gives the group lasso fit, } \alpha=1$$ gives the lasso fit).

The default value of $$\alpha$$ is 0.95.

It's possible to use the cross-validation to choose the optimal $$\alpha$$ and $$\lambda$$ parameters?

Question: How to choose the alpha parameter of SGL based on cross validation?

Thank you!

• Why not? It seems reasonable to optimize the hyper-parameter there. Mar 31, 2020 at 11:23
• @Forgottenscience Please, could you describe to me, how to do it? How to use the cross-validation to choose alpha? Apr 1, 2020 at 7:56
• Did the answer from @Edgar answer your question? If so, you might consider accepting his answer. If not, you could add a comment clarifying what advice you are still hoping for. Sep 14, 2021 at 22:29