In a LASSO regression scenario where
$y= X \beta + \epsilon$,
and the LASSO estimates are given by the following optimization problem
$ \min_\beta ||y - X \beta|| + \tau||\beta||_1$
Are there any distributional assumptions regarding the $\epsilon$?
In an OLS scenario, one would expect that the $\epsilon$ are independent and normally distributed.
Does it make any sense to analyze the residuals in a LASSO regression?
I know that the LASSO estimate can be obtained as the posterior mode under independent double-exponential priors for the $\beta_j$. But I haven't found any standard "assumption checking phase".
Thanks in advance (: