线性回归与逻辑回归
\[J(\theta)={1\over{2m}}\sum_{i=1}^{m}(h_\theta(x^{(i)})-y^{(i)})^2
\]
\[- 线性回归的损失函数的梯度
\]
{\partial\over{\partial\theta_j}}J(\theta)=\sum_{i=1}{m}(h_\theta(x)-y^{(i)})x_j\[- 逻辑回归的损失函数的梯度
\]
{\partial\over{\partial\theta_j}}J(\theta)=\sum_{i=1}{m}(h_\theta(x)-y^{(i)})x_j\[
\]
\[J(\theta)={-1\over{m}}[\sum_{i=1}^{m}y^{(i)}log(h_\theta(x^{(i)}))+(1-y^{(i)})log(1-h_\theta(x^{(i)}))]
\]
\[J(\Theta) = {1\over{m}}\sum_{i=1}^{m}\sum_{k=1}^{K} y_k^{(i)}log(h_\Theta(y_k^{(i)})) + (1 - y_k^{(i)})log(1 - h_\Theta(y_k^{(i)})) + {\lambda\over{2m}}\sum_{l}^{L-1}\sum_{i=1}^{s_l}\sum_{j=1}^{s_{l+1}}\Theta_{ji}^{l}
\]