Model and Cost Function

1 模型概述 – Model Representation

To establish notation for future use, we’ll use

• x(i)
  denote the “input” variables (living area in this example), also called input features, and
• y(i)
  denote the “output” or target variable that we are trying to predict (price).

A pair (x(i),y(i)) is called a training example
the dataset that we’ll be using to learn—a list of m training examples (x(i),y(i));i=1,…,m—is called a training set.
the superscript “(i)” in the notation is simply an index into the training set, and has nothing to do with exponentiation

• X
  denote the space of input values
• Y
  denote the space of output values

In this example

X = Y = R

To describe the supervised learning problem slightly more formally, our goal is,
given a training set, to learn afunction h : X → Yso that h(x) is a “good” predictor for the corresponding value of y.
For historical reasons, this function h is called a hypothesis. Seen pictorially, the process is therefore like this

简单的详情了一下数据集的表示方法，并且提出来h（hypothesis），即通过训练得出来的一个假设函数，通过输入x，得出来预测的结果y。并在最后详情了线性回归方程

2