Gaussian Markov random fields (MRFs) are MRFs where the variables are all jointly Gaussian. The graph structure is reflected in the sparsity pattern of the precision matrix.
This concept has the prerequisites:
- information form for multivariate Gaussians (Gaussian MRFs define constraints on the information form representation.)
- Markov random fields
Core resources (we're sorry, we haven't finished tracking down resources for this concept yet)
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 7.3, pages 254-257
- We often want to do one of the following in Gaussian MRFs:Gaussian Bayes nets , and the structure shows up in the Cholesky factorization of the covariance matrix.
- Important special cases includeuseful in low-level image processing .
- Many algorithms which are inefficient or inexact for general MRFs are efficient and exact for Gaussian MRFs. Examples include:
- inferring the mean with loopy belief propagation
- "learning the parameters:gaussian_mrf_parameter_learning
- 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