【stanford】二、supervised learning：Linear Regression

supervised learning

learn a function h : X → Y

h is called a hypothesis.

一、Linear Regression

例子中，x是二维向量，x1代表living area，x2代表bedrooms

functions/hypotheses h

设x₀ = 1，变换得

Now, given a training set, how do we pick, or learn, the parameters θ?现在变为求参数θ

One reasonable method seems to be to make h(x) close to y，

We define the cost function:定义损失函数：

   要让这个函数值最小

1、LMS algorithm：Least mean square

We want to choose θ so as to minimize J(θ).

gradient descent algorithm

α is called the learning rate.

  LMS update rule

called batch gradient descent

算法：

每次循环中每个θ,比如θ_j都要更新m次，i=1,2,…m，m为训练集元素个数。

如果m太大，则这个算法会很慢，改用随机梯度下降法