When factors are correlated (in some sense, swappable), LASSO tends to select factors who predict large values (so the $\beta$ is smaller), which are not necessarily the factor are are most predictive (big values are not necessarily good values).
This is obviously not optimal, especially when we have some a-priori knowledge about the factors.
What is often suggested is to throw away those factors which are known to be correlated with other factors. However, it is hard to figure out which one to throw away. This is also something I don't understand: if I know which factor to remove, then what's the point of feature selection?
I am wondering if there is a way to keep the feature selection more controllable. The solution I can think of is to 'normalize' the factors into Z-score, which normally distributed within [-3,3] range.
Still, I am afraid this might not be robust enough. Can anyone here give me some insights?