we have learned that when increasing the regularization parameter A in the regularized least square problem...

Transcribed Image Text:

we have learned that when increasing the regularization parameter A in the regularized least square problem 11||wy|| + where y = (y1,..., yn) ER", T (6(x₁),..., (Xn)) = RMXn, the magnitude of the optimal solution will decrease. Let the optimal solution w be W₂ = (AI+T)-¹0Ty You are asked to show that the Euclidean norm of the optimal solution ||W||2 will decrease as A increases. Hint: (1) use the result (2) for any vector u Rif VTV = I where V e Rdxd then ||Vu||2 = ||u||2 min w 2 = we have learned that when increasing the regularization parameter A in the regularized least square problem 11||wy|| + where y = (y1,..., yn) ER", T (6(x₁),..., (Xn)) = RMXn, the magnitude of the optimal solution will decrease. Let the optimal solution w be W₂ = (AI+T)-¹0Ty You are asked to show that the Euclidean norm of the optimal solution ||W||2 will decrease as A increases. Hint: (1) use the result (2) for any vector u Rif VTV = I where V e Rdxd then ||Vu||2 = ||u||2 min w 2 =