[{"source":{"position":1,"lines":["## 条件独立与图"],"changePosition":null},"target":{"position":1,"lines":["# 条件独立与图"],"changePosition":null},"type":"CHANGE"},{"source":{"position":7,"lines":["P(y,z)>0,那么在已知Z的情况下X和Y条件独立。换句话说一旦知道了Z， 那么获悉Y的值不会帮助获得X的值有任何额外信息。这就是咱们经常说的条件独立,形式化表达为$(X \\bot Y | Z)$.且独立一般有如下的性质"],"changePosition":null},"target":{"position":7,"lines":["P(y,z)>0,那么在已知Z的情况下X和Y条件独立。换句话说一旦知道了Z， 那么获悉Y的值不会帮助获得X的值有任何额外信息。这就是咱们经常说的条件独立,形式化表达为$(X \\bot Y | Z)$.且独立一般有如下的性质.或者当P满足$(X \\bot Y | Z)$，当且仅当P(X,Y|Z)=P(X|Z)\* P(Y|Z)."],"changePosition":null},"type":"CHANGE"},{"source":{"position":15,"lines":[],"changePosition":null},"target":{"position":15,"lines":["## 不同路径判断独立","### 链式结构","对于链式结构而言，","$$\begin{gathered}","p(a,c|b)=\\frac{p(a,b,c)}{p(c)} \\\\","=\\frac{p(a)p(b|a)p(c|b)}{p(c)} \\\\","=p(a|b)p(c|b)","\end{gathered}$$","从而推出a,c关于b独立， $A \\bot C|B$"],"changePosition":null},"type":"INSERT"},{"source":{"position":16,"lines":[],"changePosition":null},"target":{"position":25,"lines":["### 叉式结构","$$\begin{gathered}","p(a,c|b)=\\frac{p(a,b,c)}{p(b)} \\\\","=p(a|b)p(c|b)","\end{gathered}$$","这种情况存在，A、B不独立，但是关于条件C独立。","","### 对撞结构","如对撞结构可以得出，","$$","p(a,b,c)=p(a)p(c)p(b|a,c)","p(a,b)=p(a)* p(b)","$$","假设观测到了B，","$$\begin{gathered}","p(a,c|b)=\\frac{p(a,b,c)}{p(b)} \\\\","=\\frac{p(a)p(c)p(b|a,c)}{p(c)}\\\\","\end{gathered}$$","这种情况下， 一般ac在b的条件下不独立，"],"changePosition":null},"type":"INSERT"},{"source":{"position":57,"lines":["
"],"changePosition":null},"target":{"position":85,"lines":[""],"changePosition":null},"type":"CHANGE"},{"source":{"position":59,"lines":[],"changePosition":null},"target":{"position":87,"lines":["# 贝叶斯网络构建的方法","1. 选择变量的一个合理顺序：$x_1,x_2,……x_n$","2. 在网络中添加一个节点$x_{i}$,使之满足$p(x_{i}|parent(x_{i}))=p(x_{i}|x_1,x_2,……x_{i-1})$","3. 如果不相等则说明它们不独立,可以引出一条线,否则它们之间没有联系。","4. 然后增加一点，继续判断，直到结束。"],"changePosition":null},"type":"INSERT"}]