definition

Assume that x is a continuous random variable whose distribution depends on the category state and is expressed in the form of p(x|ω). This is the "class conditional probability" function, that is, the probability function of x when the category state is ω.

The class conditional probability function $latex P\left(X | w_{i}\right) $ refers to the probability density of the occurrence of eigenvalue X in the feature space of a known class, which refers to how the attribute X is distributed in the $latex w_{i}$ class of samples.

The difference between related concepts

$latex P\left(X | w_{1}\right) $ 、 $latex P\left(X | w_{2}\right) $ 、 $latex P\left( w_{1} | X\right) $ 、 $latex P\left( w_{2} |

$latex P\left(X | w_{1}\right) $ and $latex P\left(X | w_{2}\right) $ are the probabilities of $latex w_{1} $ and $latex w_{2} $ occurring under the same condition X. If $latex P\left(X | w_{1}\right) $ > $latex P\left(X | w_{2}\right) $ , then we can conclude that under condition X, the probability of event $latex w_{1}$ occurring is greater than that of event $latex w_{2} $.

$latex P\left( w_{1} | X\right) $ and $latex P\left( w_{2} | X\right) $ both refer to the possibility of X appearing under their respective conditions. There is no connection between the two, and it is meaningless to compare the two. $latex P\left( w_{1} | X\right) $ and $latex P\left( w_{2} | X\right) $ are issues discussed under different conditions. Even if there are only two types, $latex w_{i}$ and $latex w_{i}$ , $latex P\left( w_{1} | X\right) $ + $latex P\left( w_{2} | X\right) $ ≠1. Just because $latex P\left( w_{1} | X\right) $ is greater than $latex P\left( w_{2} | X\right) $ , it does not mean that X is more likely to be of the first type. Only by considering the factor of prior probability can we determine whether X is more likely to be of the $latex w_{i}$ type or the $latex w_{i}$ type. (See: Bayesian formula)