Exercise 3: Regularized kernel regression
The goal of this exercise to find the coefficients of regularized kernel regression model. Given $m$ training
samples $(x_i, y_i) \in \mathbb{R}^d \times \mathbb{R}$ for all $i = 1, \dots, m$ and a positive semidefinite kernel function $K(x, x') :$
$\mathbb{R}^d \times \mathbb{R}^d \to \mathbb{R}$. Follow our lecture notes to solve the following regularized optimization problem
$$
\underset{w \in \mathbb{R}^d}{\text{minimize}} \sum_{i=1}^{m} (y_i - w^T \phi(x_i))^2 + \lambda ||w||^2.
$$
Then write down the kernel regression model and explain how to make prediction for new data $x \in \mathbb{R}^d$.
Hint: Representer Theorem still holds.
