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.