Conditional Independence

Definition: 32#32 is conditionally independent of 167#167 given 168#168 if the probability distribution governing 32#32 is independent of the value of 167#167 given the value of 168#168; that is, if

169#169

more compactly, we write

170#170

Example: 171#171 is conditionally independent of 172#172, given 173#173

174#174

Naive Bayes uses cond. indep. to justify

175#175 52#52 176#176

52#52 177#177