factor graphs

(40 minutes to learn)


Markov random fields often can't reflect the full conditional independence structure of a probabilistic model. For instance, they can't encode whether the variables in a clique have a fully general interaction, or merely pairwise interactions. Factor graphs are a more fine-grained representation of Boltzmann distributions where the factors are shown explicitly in the graph.


This concept has the prerequisites:

Core resources (read/watch one of the following)


Supplemental resources (the following are optional, but you may find them useful)


See also

  • Sometimes factorization assumptions can be represented as tree-structured factor graphs when their Bayes net or MRF representations aren't tree-structured. Common examples include polytrees and chordal graphs.
  • In such cases, factor graph belief propagation can be applied to perform exact inference.