Probabilistic Graphical Model

When we represent factorization of probability distribution with a graph, we call it graphical model or structured probabilistic model.

Graphical models can be directed or undirected.

Directed models represent factorization using conditional probability distributions. For each RV there is a factor with conditional distribution over the RV node's parents.

Undirected models represent factorization using set of functions that assign unnormalized probablities to cliques of RVs. For each clique (set of nodes all connected to each other), say \(x_1, ..., x_k\), we have a factor \(\phi(x_1, ... x_k)\). Then the product of factors can be divided by a normalization constant.