Basis Function
[Overfitting](https://texonom.com/overfitting-24c3b183372845e8999ad7f7a0ba5035) 


## Feature Map $\phi(x)$, Basis Function $h(x)$
$$h_\theta(x) = \Sigma_{l=1}^L\theta_l\phi_l(x) = \theta^T\phi(x)$$
we can extend the linear regression into a linear combination of basis functions
$${R^d \rightarrow R} \;\; (x \in R^d)$$
- polynomial basis $x^l$
- gaussian basis $exp(-\frac{||x - \mu_l||^2}{2\sigma^2})$




### Using nonlinear basis functions, we allow the function to be nonlinear








