# factor graphs

(40 minutes to learn)

## Summary

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.

## Context

This concept has the prerequisites:

- Markov random fields (Factor graphs are a more fine-grained notation for MRFs.)

## Core resources (read/watch one of the following)

## -Paid-

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 8.4.3, pages 399-402

Additional dependencies:

- Bayesian networks

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

## -Paid-

→ Probabilistic Graphical Models: Principles and Techniques

A very comprehensive textbook for a graduate-level course on probabilistic AI.

Location:
Section 4.4.1.1, pages 123-124

## 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.