I have a non-negativity constrained LASSO problem like this:

min: $||Cx-b||_2^2 + \lambda||x||_1$

subject to: $x\geq0$

where C is a matrix, and x and b are column vectors. Now I want to use cross-validation to determine the regularization parameter $\lambda$. I want to use generalized cross-validation because it requires less computation time, but I don't know how to implement for my problem.

Golub et al. has a paper on generalized cross-validation (see the paper here), but the influence matrix $A(\lambda)$ in page 2 equation 1.5 seems only designed for ridge problem. I am just wondering how to do something similar to LASSO problem and with non-negativity constraint.

Any hint is greatly appreciated!


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