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zhangy 2025-06-05 00:41:38 +00:00
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@ -11,7 +11,7 @@
- 交叉熵 (cross entropy): $H(p,q)=\sum -p(x_i) \log q(x_i)$ - 交叉熵 (cross entropy): $H(p,q)=\sum -p(x_i) \log q(x_i)$
- 相对熵 (relative entropy) 或者 KL 散度 (Kullback-Leibler divergence, KLD): $D_{KL}(p||q):=H(p,q)-H(p)= \sum -p(x_i)\log \frac{q(x_i)}{p(x_i)}$ - 相对熵 (relative entropy) 或者 KL 散度 (Kullback-Leibler divergence, KLD): $D_{KL}(p||q):=H(p,q)-H(p)= \sum -p(x_i)\log \frac{q(x_i)}{p(x_i)}$
- $g(X,Y)=D_{KL}(p(x,y)||p(x)p(y))$ - $g(X,Y)=D_{KL}(p(x,y)||p(x)p(y))$
- JS 散度：$JS:=1/2 ( D_{KL}(p||m) + D_{KL}(q||m) )$, 这里$m=(p+q)/2$。 p和q支撑集不相交时，JS 散度为一个常数 log2 - JS 散度：$JS:=1/2 ( D_{KL}(p||m) + D_{KL}(q||m) )$, 这里$m=(p+q)/2 $ 。 p和q支撑集不相交时，JS 散度为一个常数 log2
- 最小化交叉熵=最小化KL=极大似然 - 最小化交叉熵=最小化KL=极大似然
### Bias-Variance tradeoff ### Bias-Variance tradeoff