# Gaussian MRFs

## Summary

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.

## Context

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)

## -Paid-

→ 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

## See also

- We often want to do one of the following in Gaussian MRFs: There are also Gaussian Bayes nets , and the structure shows up in the Cholesky factorization of the covariance matrix.
- Important special cases include Gaussian conditional random fields (CRFs) are useful 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