Recency weighted regression

[itooam]

Suppose I could just transform the weight matrix into a vector do a transpose then do a cross product (not sure how to present that in algebraic form but think that is the solution)!?

[itooam]

* I meant "inner" product above NOT cross product.

[itooam]

Scrap what I wrote above about large datasets causing havoc for the weight matrix. I found Octave already knows about such problems and has support for sparse matrices... very useful

[magdon]

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.

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?

[itooam]

Thanks Magdon, I always manage to make things so much more complicated than they need to be. That equation you posted would have saved me hours - and it is so simple - why didn't I think of it? Instead I went the long way round, not a total loss though as has been a great learning curve for me

I tried your approach and compared to my workings (in one of my previous posts):


and for all my tests I am getting the same . So this is great news as confirms my formula was correct too .

Many thanks, I can't say enough how much your help is appreciated.