I implemented multi-task lasso regression and it works well in CVX. Basically I’m regularizing 4 regression models together.
minimize(square_pos(norm(A*x-Y)) + Lambda * norm(x,1)
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?
minimize(square_pos(norm(Ax-Y)) + Lambda * norm(x,1) + OmegA * (sum(sqrt(sum((x . Binding_matrix’).^2, 2))))