performing a least squares with regularisation in matlab

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cgo
cgo le 13 Juil 2018
Commenté : Sterling Baird le 23 Sep 2020
I have data sets X (2n by 8) and Y(2n by 1). I want to find the coefficients a so that Y = Xa. So we can perform a = X\Y (as a least squares minimisation).
I wanted to ask if it possible to proceed with a form of regularisation (L1 or something simple) from this?
Please help.

Réponses (2)

Diwakar
Diwakar le 13 Juil 2018
My understanding of your problem is that you want to find the coefficient a. So in order to implement optimization you can implement average of sum of least squares as shown below.
Loss= ((Y-X*a)'*(Y-X*a))/(2*n);
The above shown function is a vectorized implementation of the squared error loss function. So this can be minimized in order to get the optimal value of a. If you want to fit a curve to this then any form of regularization should be fine.
Hope this helps
Cheers!
  1 commentaire
Sterling Baird
Sterling Baird le 23 Sep 2020
How would you actually implement the regularization though?

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Bruno Luong
Bruno Luong le 23 Sep 2020
Modifié(e) : Bruno Luong le 23 Sep 2020
Simpless method:
n = size(X,2); % 8
lambda = 1e-6; % <= regularization parameter, 0 no regularization, larger value stronger regularized solution
a = [X; lambda*eye(n)] \ [Y; zeros(n,1)]
  1 commentaire
Sterling Baird
Sterling Baird le 23 Sep 2020
Hi Bruno, thank you! That helps out quite a bit.

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