(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:
- Markov random fields (Factor graphs are a more fine-grained notation for MRFs.)
Core resources (read/watch one of the following)
→ 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
- Bayesian networks
Supplemental resources (the following are optional, but you may find them useful)
→ Probabilistic Graphical Models: Principles and Techniques
A very comprehensive textbook for a graduate-level course on probabilistic AI.
Location: Section 220.127.116.11, pages 123-124
- 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.
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation