mathematics_basic_for_ML

算术平均：
$$average = \frac{1}{4}(a+b+c+d)$$

几何平均：
$$ average = \sqrt4 $$

调和平均：更重视较小值
$$\begin{aligned} average = \frac{2ab}{a+b} \ \frac{1}{average} = \frac{1}{2}(\frac{1}{a} + \frac{1}{b}) \end{aligned}$$

加权调和平均：
$$\begin{aligned} average_\beta = \frac{(1+\beta^2)\times a \times b}{(\beta^2 \times a) + b} \ \frac{1}{average_\beta} = \frac{1}{1+\beta^2}(\frac{1}{a} + \frac{\beta^2}{b}) \end{aligned}$$

$\beta < 1$：更注重a
$\beta = 1$：相当于调和平均
$\beta > 1$：更注重b