Question 8: Consider a kernel regression problem on the following dat…

Consider a kernel regression problem on the following dataset with two features:

$\{(x_1, y_1), (x_2, y_2), (x_3, y_3)\}$

where:

$x_1 = \begin{bmatrix} 1 & 2 \end{bmatrix}^T, y_1 = 3, \quad x_2 = \begin{bmatrix} 2 & 3 \end{bmatrix}^T, y_2 = 5, \quad x_3 = \begin{bmatrix} 3 & 4 \end{bmatrix}^T, y_3 = 7$

The kernel function is given as:

$K(x, x') = (1 + x^\top x')^2$

and the optimal coefficients $\alpha_i$ are given as:

$\alpha = \begin{bmatrix} 0.5 & 1.0 & 1.5 \end{bmatrix}^T.$

Then, what will be the predicted value for the data point $\begin{bmatrix} 2 & 2 \end{bmatrix}^T$?