Day1 机器学习基本概念和梯度下降

机器学习定义

　　Arthur Samuel:the field of study that gives computers the ability to learn without being explicitly programmed.

　　Tom Mitchell:A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.

机器学习常用算法

　　监督学习(Supervised learning):To predict the result by analyzing some correct relationship between the input and the output.模型如下：

                

　　　　回归问题("regression"):we are trying to predict results within a continuous output.

　　　　分类问题("classification"): we are instead trying to predict results in a discrete output. 

　　非监督学习(Unsupervised learning):To approach problems with little or no idea what our results should look like. 

代价函数Cost Function

　　A function used to measure the accuracy of our hypothesis function.

　　We can use a cost function like

           

　　Our target is to find a value of θ0 and θ1 to  get the min J

 梯度下降算法Gradient Descent Algorithm

　　 repeat until convergence:{

            

　　　　　　}

　　　　α : 学习速率(learning rate).

　　　　　　if α is too small,gradient descent can be slow .

　　　　　　if α is too large,gradient descent can overshoot the minimum.It may fail to converge,or even diverge.

　　算法中θ0和θ1是同时改变的：