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GO Classes DPP | ML |RIDGE REGRESSION

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Assuming that in the constrained version of ridge regression optimization problem, following are the weight vectors to be considered, along with the mean squared error (MSE) produced by each:

$$
\begin{aligned}
& w_1=[2,2,3,1], \text { MSE }=3 \\
& w_2=[1,1,3,1], \text { MSE }=5 \\
& w_3=[3,2,4,1], \text { MSE }=8 \\
& w_4=[1,2,1,1], \text { MSE }=9
\end{aligned}
$$


If the value of $\theta$ is 13 , which of the following weight vectors will be selected as the final weight vector by ridge regression?

Note: $\|w\|^2 \leq \theta$

  1. W1
     
  2. W2
     
  3. W3
     
  4. W4

1 Answer

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We need to minimize MSE such that $\|w\|^2 \leq \theta$

$$
\begin{aligned}
& \left\|w_1\right\|^2=18,\left\|w_2\right\|^2=12,\left\|w_3\right\|^2=30,\left\|w_4\right\|^2=7 \\
& \|w\|^2 \leq 13 \text { for } w_2 \text { and } w_4
\end{aligned}
$$

However, the MSE for $w_2$ is lesser than $w_4$.

Hence, $w_2$ will be chosen.
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