Linear regression with one varia

2020-01-27 本文已影响0人 spraysss

Housing Prices

Hypothesis:

$h_{\theta}(x)=\theta_0+\theta_1x$

Parameters:

$\theta_0\theta_1$

Cost function:

Squared error
$J(\theta_0,\theta_1)=\frac{1}{2m}\sum_{i=1}^{m}(h_\theta(x^i)-y^i)^2$

Goal

Min $J(\theta_0,\theta_1)$

Gradient descent

start with some $\theta_0,\theta_1$
keep changing $\theta_0,\theta_1$ to reduce $J(\theta_0,\theta_1)$ until we hopefully end up at a minimum

Gradient descent algorithm

repeat until convergence {
$\space \theta_j:=\theta_j-\alpha\frac{\partial}{\partial\theta_j}J(\theta_0,\theta_1) (for \space j=0 \space and \space j=1)$
}
Note : the Correct way is simultaneous update

$temp0:=\theta_0:=\theta_0-\alpha\frac{\partial}{\partial\theta_0}J(\theta_0,\theta_1)$
$temp1:=\theta_1:=\theta_1-\alpha\frac{\partial}{\partial\theta_1}J(\theta_0,\theta_1)$
$\theta_0:=temp0$
$\theta_1:=temp1$