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Old 08-27-2012, 01:08 PM
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magdon magdon is offline
Join Date: Aug 2009
Location: Troy, NY, USA.
Posts: 597
Default Re: Recency weighted regression

Yes, there is a closed form solution which is obtained by taking the \alpha_t into the square:


This is exactly an unscaled linear regression problem where you have rescaled each data point (\mathbf{x}_t,y_t) by \sqrt{\alpha_t}. So, after you rescale your data in this way, you can just run your old regression algorithm without the weightings.

Originally Posted by itooam View Post
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 \alpha 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:

W_{reg} = (Z^{T} Z+\lambda I)^{-1}Z^Ty

I am not sure where \alpha would end up in the above, the derivation is beyond me mathematically?
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