一元线性回归

回归函数:

$$f_{w,b}(x) = wx + b$$

代价函数:

$$J(w,b) = \frac{1}{2m}\sum_{i=1}^m(f_{w,b}(x_i)-y_i)^2$$

梯度下降法同时更新w和b:

$$tmp_w=w-\alpha\frac{\partial J(w,b)}{\partial w}=w-\alpha\frac{1}{m}\sum_{i=1}^m(f_{w,b}(x_i)-y_i)x_i$$ $$tmp_b=b-\alpha\frac{\partial J(w,b)}{\partial b}=b-\alpha\frac{1}{m}\sum_{i=1}^m(f_{w,b}(x_i)-y_i)$$ $$w = tmp_w$$ $$b = tmp_b$$

\(\alpha\)是学习率,用来控制下降幅度