Probabilistic Graphical Models

• A probabilistic graphical model is a graph that describes a probability distribution.

  • In a PGM, nodes correspond to variables of the joint probability.
  • An edge between two nodes means the corresponding variables are not conditionally independent.
  • In a directed graphical model, the directed edges indicate conditioning. An arc indicates the factor .

• A variant of this is a factor graph which is a bipartite graph where nodes are either variables or factors and edges connect between a variable and a factor.

  • An edge indicates that the variable is a part of the corresponding factor.
  • If the set of factors is , then the joint probability distribution can be written as
    Where denotes the vector of neighboring variable nodes to factor node .

• PGMs allow us to perform inferences much more efficiently since we can focus on only computing factors.