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2. (Textbook 6.3 + 6.4, 20 pt) Consider the ridge regression min (ridge

regression) 1 with tuning parameter λ ě 0 and the constrained version of LASSO min β }Y ´ Xβ} (LASSO) with tuning parameter s ě 0. As λ and s increases from 0 respectively, choose which of (i) to (v) is correct for: (a) training RSS, (b) test RSS, (c) variance, and (d) (squared) bias.

(i) Increase initially, and then eventually start decreasing in an inverted U shape. (ii) Decrease initially, and then eventually start increasing in a U shape. (iii) Steadily increase. (iv) Steadily decrease. (v) Remain constant.

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MachineLearning2.png

MachineLearning2.png

2. (Textbook 6.3 + 6.4, 20 pt) Consider the ridge regression P
inain HY — Xfi||§ + A 2 r3}; (ridge regression)
k=1 with tuning parameter /\ 2 0 and the constrained version of LASSO min llY—Xfilli
’3 p (LASSO)
at. Z |fik| S 3
33:1 with tuning parameter s 2 0. As /\ and 8 increases from 0 respectively, indicate which of (i) to (v) is correct for: (a) training RSS, (b) test RSS, (c) variance, and (d) (squared) bias. Justify your answer.
(i) Increase initially, and then eventually start decreasing in an inverted U shape. (ii) Decrease initially, and then eventually start increasing in a U shape. (iii) Steadily increase. (iv) Steadily decrease. (v) Remain constant.

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