# Is the LASSO also a subset selection method?

I have got a question about the LASSO regularisation method, this method is usually used in machine learning and multivariate statistics to avoid the overfitting and hence, get better predictions. The "penalised" log-likelihood of a LASSO model is given by:

$\underset{\beta}{\text{argmax}} \qquad l(\beta) - \lambda \cdot \sum_{j=1}^{p}\left | \beta _{j} |\right.$

where $l$ is the log-likelihood and $\beta$ are the regression coefficient. Usually the size of the regression coefficients included in the fitted model are shrink. However, I have seen some publications that use the "full" sized chosen parameters later on in a model, instead of the "shrink" sized parameters. Thus, they are using the LASSO as a subset selection method akin to univariate analysis. Would you agree that that is not a correct approach?

• There have been some related discussions here, you might search for them with the right keywords. Perhaps this exact question has not been asked, but some related ones have been. – Richard Hardy Apr 12 '18 at 7:30
• Look for "relaxed LASSO". – Scortchi - Reinstate Monica Apr 12 '18 at 9:46
• Hi, yes I see what you mean. I checked the relaxed LASSO and it is exactly what I was looking for. Thank you. – Carlos ST Apr 12 '18 at 19:22