lasso sparse regression on Y matrix

Hello,

I have a data matrix Y (N x M) on which I want to fit a GLM specified by the design matrix X (N x P). An easy way of estimating the beta matrix would be employing an OLS estimator:

B = (inv(X'*X)\X')*Y;

However, in the scenario I face, a sparse regression approach might be a more sensible choice. My first pick would be an L1 regularization approach (lasso regression), but for the life of me I cannot find a useful matlab implementation. That is because /all/ MatLab implementations of lasso I have come across so far (built-in and custom-written ones) do require Y to be a vector of observations, but cant handle matrices as input. Consequently, this only gets me a B vector (P X 1) as output, whereas B is supposed to be a P x M matrix.

Any suggestions on how to fix this are highly appreciated.

Regards

[Matt J]

I assume you mean

B = inv(X'*X)*X'*Y;

Answer 1

[Matt J]

Can't you just use a loop over the columns of Y, fitting one column at a time?

Or, you could reformulate as a block diagonal system

 XX=kron(speye(M), X);
 YY=Y(:);

and solve the equivalent single-vector system

 XX*beta=YY;

I expect the loop would be better/faster, because it reduces the problem to simpler, lower-dimensional problems.