Given y E R”, consider ridge regression with predictor matrix X = Inxn, i.e., Y = > | For the lasso with identity predic
Posted: Thu Jan 13, 2022 5:48 am
Given y E R”, consider ridge regression with predictor matrix X = Inxn, i.e., Y = > | For the lasso with identity predictor matrix, = ĝlasso = argmin ||Y – B112 + 1 || B||1 BER" n n = = argmin (yi – B;)2 +11Bi, BERN i=1 PROVE THE SOLUTION IS: Slasso Yi + 1/2 Yi < -1/2 0 |yi| < 1/2, i = 1, ... n. yi Yi – 1/2 Yi > 1/2 i =