For a design matrix X = RnXP and observations y ER", the Lasso estimator is defined as 1 BLasso (A) E arg miny - X||+||B||1 BERP (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 BLasso (A) ST(y, A) := sign(y) max(|y| - A, 0). = The function ST is called the Soft-Thresholding operator. Plot on the same graphics, the functions yy and y ST(y, ) for y = R for some fixed values of (for example two values of A 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 y = R. Discuss and illustrate some key differences between Lasso and Ridge. Activ.