Solving Lasso. (30 points) For a design matrix XRnp and observations yRn, the Lasso estimator is defined as Lasso()Rpargmin21yX22+1. (a) Single parameter setup for Lasso. (10 points) Show that for the identity matrix X=Id and p=1, the Lasso solution is given by Lasso()=ST(y,):=sign(y)max(y,0). The function ST is called the Soft-Thresholding operator. Plot on the same graphics, the functions yy and yST(y,) for yR for some fixed values of (for example two values of should be fine in order to get an intuition on how the model parameters are set to zero). Write the Ridge estimator when X= Id and yR. Discuss and illustrate some key differences between Lasso and Ridge