In probability theory and statistics, a graphical model (GM) represents dependencies among random variables by a graph in which each random variable is a node.
In the simplest case, the network structure of the model is a directed acyclic graph. Then the GM represents a factorization of the joint probability of all random variables. More precisely, if the random variables are X_1 through X_n, then the joint probability P(X_1,...,X_n) is equal to the product of the conditional probabilities P(X_i | parents of X_i) for all i=1,...,n. In other words, the joint distribution factors into a product of conditional distributions. The graph structure indicates direct dependencies among random variables. Any two nodes that are not in a descendant/ancestor relationship are conditionally independent given the values of their parents.