吴恩达机器学习第一章总结

机器学习分为监督学习（supervised learning) 无监督学习(unsupervised learning）

强化学习(reinforcement learning) 推荐系统(recommender systems)

1.supervised learning

regression（回归）对应 predict continuous

classification(分类）对应 discrete value

2.unsupervised learning

no label find structure

cluster 聚类

Notation:

m: number of training example
x: input feature
y: output variable
$(x^i,y^i)$
h=hypothesis (x to y function)

linear regression(线性回归）

h(x)=θ₀+θ₁*x;

cost function

$$J({\theta }_0,{\theta }_1)=\frac{1}{2m}\sum _{i=1}^m(h_{\theta }(x^{(i)})-y^{(i)}{)}^2$$

gradient descent(梯度下降)

同时更新

$${\theta }_j:={\theta }_j-\alpha \frac{\partial }{\partial {\theta }_j}J({\theta }_0,{\theta }_1)$$

$\alpha$太小就很慢
太大就不会收敛

repeat until converge{

$${\theta }_0:={\theta }_0-\alpha \frac{1}{m}\sum _{i=1}^m(h_{\theta }(x^i)-y^i)$$
$${\theta }_1:={\theta }_1-\alpha \frac{1}{m}\sum _{i=1}^m(h_{\theta }(x^i)-y^i)x^i$$

}

update simultaneously get local minimum
counvex foucntion（凸函数） 一定有只有一个解 become global minimum