From 6b7b6ea60edb080b1d63f8c281ff4f38e13f823d Mon Sep 17 00:00:00 2001
From: zhangy <mathgeometry@163.com>
Date: Thu, 5 Jun 2025 00:41:38 +0000
Subject: [PATCH] =?UTF-8?q?=E6=9B=B4=E6=96=B0=20test.md?=
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 - 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): $D_{KL}(p||q):=H(p,q)-H(p)= \sum -p(x_i)\log \frac{q(x_i)}{p(x_i)}$
 - $g(X,Y)=D_{KL}(p(x,y)||p(x)p(y))$
-- 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
 
 ### Bias-Variance tradeoff