Cost Function
Model Representation
m = Number of training examples
x's = "input" variable / features
y's = "output" variable / "targer" variable
h instand for hypothesis h represent a function
How do we represent h?
Cost Function
- minimize
- 代价函数（平方误差函数，平方误差代价函数）解决回归问题最好的手段
Hypothesis:
Cost Function:
Goal:
Cost Function
Simplified:
对于线性回归来说
- 一维的代价函数是一个弓形
- 三维的代价函数和一维的代价函数一样都是一个弓形
contour plot or contour figure:轮廓图
Gradient descent
Gradient descent can be used in more common cost function ,not only in two parameter
Outline:
Start with some
Keep changingto reduce J(
Until we hopefully end up at a minimum
Gradient descent algorithm:
repeta until convergence {(for
=0 and
=1)}
is a mumber called learning rate, which control the length of our step in Gradient descent.
Correct: Simultaneous update
temp0:=
temp1:=
Incorrect:
temp0:=
temp1:=
同时更新
Gradient descent's characteristics
if
if
As we approach a local minimum, gradient descent will automatically take smaller steps. So, no need to decraser
Gradient Descent For Liner Reg
convex function
"Batch" Gradient Descent: Each step of gradient descent uses all the training examples.
