archwalker 5 anos atrás
pai
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3320859cef
1 arquivos alterados com 1 adições e 1 exclusões
  1. 1 1
      docs/chapter12/chapter12.md

+ 1 - 1
docs/chapter12/chapter12.md

@@ -559,7 +559,7 @@ $$
 $$
 \begin{aligned} \widehat{E}(h) &=\frac{1}{m} \sum_{i=1}^{m} \mathbb{I}\left(h\left(\boldsymbol{x}_{i}\right) \neq y_{i}\right) \\ &=\frac{1}{m} \sum_{i=1}^{m} \frac{1-y_{i} h\left(\boldsymbol{x}_{i}\right)}{2} \\ &=\frac{1}{2}-\frac{1}{2 m} \sum_{i=1}^{m} y_{i} h\left(\boldsymbol{x}_{i}\right) \end{aligned}
 $$
-[解析]:这里解释从第一步到第二步的推导,因为前提假设是2分类问题,$y_k\in\{-1, +1\}$,因此$\mathbb{I}\left(h(x_i)\neq y_i\right)\equiv \frac{1-y_i h(x_i)}{2}$。这是因为假如$y_i=+1, h(x_i)=+1$或$y_i=-1, h(x_i)=-1$,有$\mathbb{I}\left(h(x_i)\neq y_i\right)=1= \frac{1-y_i h(x_i)}{2}$;反之,假如$y_i=-1, h(x_i)=+1$或$y_i=+1, h(x_i)=-1$,有$\mathbb{I}\left(h(x_i)\neq y_i\right)=0= \frac{1-y_i h(x_i)}{2}$。
+[解析]:这里解释从第一步到第二步的推导,因为前提假设是2分类问题,$y_k\in\{-1, +1\}$,因此$\mathbb{I}\left(h(x_i)\neq y_i\right)\equiv \frac{1-y_i h(x_i)}{2}$。这是因为假如$y_i=+1, h(x_i)=+1$或$y_i=-1, h(x_i)=-1$,有$\mathbb{I}\left(h(x_i)\neq y_i\right)=0= \frac{1-y_i h(x_i)}{2}$;反之,假如$y_i=-1, h(x_i)=+1$或$y_i=+1, h(x_i)=-1$,有$\mathbb{I}\left(h(x_i)\neq y_i\right)=1= \frac{1-y_i h(x_i)}{2}$。