Kernel Regression

• We can use linear regression for non-linear data using high dimensional quadratic line
• The problem is we don't know which polynomial to use
• So we use Kernel Regression
• Kernel Regression is a Non-parametric Method

[!def] Kernel Regression Formula
$$
f(x) = \frac{1}{N} \sum_{i=1}^N w_i y_i
$$
where,
$$
w_i = \frac{N ; k(\frac{x_i - x}{b})}{\sum_{l=1}^N k(\frac{x_l-x}{b})}
$$
$k()$ most frequently used gaussian kernel
$$
k(z) = \frac{1}{\sqrt{2 \pi}} \exp (\frac{-z^2}{2})
$$

• The function k() is a kernel function, which works as a similarity function.