How to compute second norm of each row of matrix inside of CVX objective function?

1

Hi all,

I implemented multi-task lasso regression and it works well in CVX. Basically I’m regularizing 4 regression models together.
cvx_begin quiet
variable x(50,4)
minimize(square_pos(norm(A*x-Y)) + Lambda * norm(x,1)

cvx_end

now I want to add other regularization term which regularize second norm for each features across different regression model. in other word, if feature V is belong to specific group, its vector of coefficients across different regularized by second norm. I have a binary matrix called Group which indicate which feature coefficient vector(here the size of vector for every feature is 4 because we have 4 model) should regularized across different models. I tried to add this regularization like this, but seems CVX does not accept sqrt .
Would someone help me with this?

cvx_begin quiet
variable x(50,4)
minimize(square_pos(norm(Ax-Y)) + Lambda * norm(x,1) + OmegA * (sum(sqrt(sum((x . Binding_matrix’).^2, 2))))

cvx_end

2

Check out the norms function in CVX, either from the users guide or by typing help norms at the command prompt.

1 Like
3

THANKS.
Does my implementation looks fine? Because I’m not getting proper results. I would assume that, L2 norm regularization force smoothness for the coefficients of features across different model, but in reality I’m not getting that.