# Gaussian variable elimination

## Summary

Marginalization in Gaussian MRFs can be performed in cubic time by inverting a matrix, but this is too slow for some applications. If the model has the right structure, variable elimination can result in a big speedup.

## Context

This concept has the prerequisites:

- Gaussian MRFs (Gaussian variable elimination is an inference algorithm for Gaussian MRFs.)
- variable elimination
- computations on multivariate Gaussians (Gaussian MRF inference is defined in terms of operations on multivariate Gaussians.)

## 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 14.2-14.2.2, pages 608-612

## See also

- If we run multiple queries, variable elimination involves redundant computations. Belief propagation gives a way of sharing these computations.
- Kalman smoothing can be seen as a special case of Gaussian BP.
- Gaussian variable elimination is equivalent to Gaussian elimination.