Marginal Distribution

Marginal distribution refers to the probability distribution of only some variables among multidimensional random variables in probability theory and statistics.

definition

Suppose there is a probability distribution associated with two variables: $latex P(x, y) $

The marginal distribution about one of the variables is then the conditional probability distribution given the other variables: $latex P(x)=\sum_{y} P(x, y)=\sum_{y} P(x | y) P(y) $

In this marginal distribution, we obtain a probability distribution only about one variable, without considering the influence of another variable, which actually performs a dimensionality reduction operation.

In practical applications, such as artificial neural networks, neurons are interconnected, and when calculating their respective parameters, the marginal distribution is used to calculate the value of a specific neuron (variable).

Reference source: https://zh.wikipedia.org/wiki/Edge distribution