各模型常用的损失函数

各模型常用的损失函数

线性模型

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

Logistic Regression

$$\begin{gathered} J(\theta )=\frac{1}{m}\sum _{i=1}^{m}Cost(h_{\theta }(x^{(i)}),y^{(i)}) \\ Cost(h_{\theta }(x),y)=-log(h_{\theta }(x))ify=1 \\ Cost(h_{\theta }(x),y)=-log(1-h_{\theta }(x))ify=0 \end{gathered}$$
该损失函数可以简写为：
$$J(\theta )=-\frac{1}{m}\sum _{i=1}^m[y^{(i)}log(h_{\theta }(x^{(i)}))+(1-y^{(i)})log(1-h_{\theta }(x^{(i)}))]$$

---

持续更新