线性回归算法

例子还是之前预测房价：

Notation:

• m = Number of training examples
• x’s = “input” variable/features 特征量
• y’s = “output” variable/ “target” variable 目标变量

Estimated price/hypothesis

$\color{red}h_\Theta (x) =\Theta_0+\Theta_1x$hΘ​(x)=Θ0​+Θ1​x

$h_\Theta (x)$hΘ​(x) shorthand h(x)

代价函数(cost function)

$\color{red}J(\Theta_0,\Theta_1)=\frac{1}{2m}\sum_{i=1}^{m}(h_\Theta(x^{(i)})-y^{(i)})^2$J(Θ0​,Θ1​)=2m1​∑i=1m​(hΘ​(x(i))−y(i))2

平方误差的代价函数是解决线性回归问题最常用的手段.

优化目标(Goal)

$minimize_{\Theta_0,\Theta_1}J(\Theta_0,\Theta_1)$minimizeΘ0​,Θ1​​J(Θ0​,Θ1​)

代价函数的轮廓图：