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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!

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  • $\begingroup$ Why not? It seems reasonable to optimize the hyper-parameter there. $\endgroup$ Mar 31, 2020 at 11:23
  • $\begingroup$ @Forgottenscience Please, could you describe to me, how to do it? How to use the cross-validation to choose alpha? $\endgroup$ Apr 1, 2020 at 7:56
  • $\begingroup$ 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. $\endgroup$ Sep 14, 2021 at 22:29

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I strongly recommend to use R and the package "SGL" to compute sparse-group lasso, which is maintained by the authors of the SGL paper themselves.

Within the package, you have the function "cvSGL", which does the cross-validation for you.

Be advised, the SGL-package is not optimized for speed and has different default parameters (number of iterations, minimum error for convergence) than the LASSO/Elastic-Net implementations within the "glmnet" package, so SGL-results are not directly comparable with LASSO results.

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