Github user mengxr commented on the pull request:
https://github.com/apache/spark/pull/11610#issuecomment-196486264
@iyounus @dbtsai The normal equation approach will fail if the matrix A is
rank-deficient. It happens when there are constant columns. However, more
generally, it happens when there are linearly dependent columns in the training
dataset. So this PR solves one case but it is not a general solution. We can
try two approaches:
1. Distributed QR/SVD to deal with rank deficiency. QR requires pivoting.
SVD might be an easier approach for us, though a little expensive.
2. Add a small positive number, e.g., `1e-8`, to the diagonal when AtA is
rank deficient. This should solve the numerical issue but returns a less
accurate solution. However, it is always good to apply regularization. I
believe this won't make the model worse.
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