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 $latex P\left(X | w\_{i}\right)$latexP(X∣w_i) 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 $latex w\_{i}$latexw_i class of samples.

The difference between related concepts

$latex P\left(X | w\_{1}\right)$latexP(X∣w_1) 、 $latex P\left(X | w\_{2}\right)$latexP(X∣w_2) 、 $latex P\left( w\_{1} | X\right)$latexP(w_1∣X) 、 $latex P\left( w_{2} |

$latex P\left(X | w\_{1}\right)$latexP(X∣w_1) and $latex P\left(X | w\_{2}\right)$latexP(X∣w_2) are the probabilities of $latex w\_{1}$latexw_1 and $latex w\_{2}$latexw_2 occurring under the same condition X. If $latex P\left(X | w\_{1}\right)$latexP(X∣w_1) > $latex P\left(X | w\_{2}\right)$latexP(X∣w_2) , then we can conclude that under condition X, the probability of event $latex w\_{1}$latexw_1 occurring is greater than that of event $latex w\_{2}$latexw_2.

$latex P\left( w\_{1} | X\right)$latexP(w_1∣X) and $latex P\left( w\_{2} | X\right)$latexP(w_2∣X) 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. $latex P\left( w\_{1} | X\right)$latexP(w_1∣X) and $latex P\left( w\_{2} | X\right)$latexP(w_2∣X) are issues discussed under different conditions. Even if there are only two types, $latex w\_{i}$latexw_i and $latex w\_{i}$latexw_i , $latex P\left( w\_{1} | X\right)$latexP(w_1∣X) + $latex P\left( w\_{2} | X\right)$latexP(w_2∣X) ≠1. Just because $latex P\left( w\_{1} | X\right)$latexP(w_1∣X) is greater than $latex P\left( w\_{2} | X\right)$latexP(w_2∣X) , 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 $latex w\_{i}$latexw_i type or the $latex w\_{i}$latexw_i type. (See: Bayesian formula)