performing a least squares with regularisation in matlab

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.

Answer 1

[Diwakar]

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!

[Sterling Baird]

How would you actually implement the regularization though?

Answer 2

[Bruno Luong]

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)]

[Sterling Baird]

Hi Bruno, thank you! That helps out quite a bit.