I am working with a data set that has 18500 dimensions and 450 observations(p>>n). I am coding on R and I am looking at using LASSO, Ridge and Elastic net regression. I am also looking into performing some form of variable selection with PCA or SVD. I know that I want to compare different models, first using Ridge, LASSO and Elastic Net on the full data set. I am considering comparing these models to a model fitted after performing PCA or SVD. In what manner should I compare my models considering the fact that I am attempting to perform a prediction task? I am considering comparing MSE values as well as the correlation between y and y_hat values.
I was also wondering if anybody could recommend a place where I could find some useful code and packages in order to undertake this task in R? Any help would be much appreciated. Thanks