So I'm using lasso logistic regression to classify my data.
My data matrix $X$ has dimension $n\times p$ for $p >> n$.
As $p$ is on the order of a billion, I expect to face some computational challenges when trying to run lasso logistic regression.
If I'm only interested in predictive performance, and I don't care about inference, is there any drawback to taking the SVD of
and then simply applying lasso logistic regression to $U$?
As far as I can tell, all I've done is do a change of basis so that I'm only considering the $n-1$ dimensional affine space spanned by my data, and thus my classification algorithm should perform just as well.
It does appear that the above is correct, see the related question,