Elastic Net Collinearity When performing linear regression it is often assumed that the predictors are independent with Gaussian noise:
\begin{equation}
Y = X\beta + \epsilon \quad
\epsilon \sim \mathcal{N}(0, \sigma)
\end{equation}
If there is collinearity between them, one could instead transform the data to use principal component regression so that the predictors are orthogonal.
When doing an elastic net regression, should we also assume that the predictors are independent? If so, I haven't come across resources where the data is transformed into its principal directions first.

There is no such assumption about linear regression features. This is a common misconception that I believe comes from the assumption of uncorrelated errors in the Gauss-Markov theorem and mistaking that to be about the observable features rather than unobservable errors.
You don’t need independent features to run elastic net regression, either. In many regards, elastic net is just an estimation alternative to ordinary least squares that might have desirable properties in some circumstances (such as better out-of-sample performance than OLS).
