Yes, there is a closed form solution which is obtained by taking the
into the square:
This is exactly an unscaled linear regression problem where you have rescaled each data point
by
. So, after you rescale your data in this way, you can just run your old regression algorithm without the weightings.
Quote:
Originally Posted by itooam
Thank you for all your help it has been really appreciated. I have one final question, do you know if there is a closed form solution to
(assuming is a vector with the same number of rows as x?)
i.e., the closed form solution as used for linear regression and regularization  copied from lecture notes is this:
I am not sure where would end up in the above, the derivation is beyond me mathematically?
