# information form for multivariate Gaussians

(40 minutes to learn)

## Summary

While we normally represent multivariate Gaussians in terms of their mean and covariance, information form is often a useful alternative. The distribution is represented in terms of a quadratic "energy function." This representation is convenient for conditioning, and is the basis for Gaussian Markov random fields.

## Context

This concept has the prerequisites:

## Core resources (read/watch one of the following)

## -Paid-

→ Probabilistic Graphical Models: Principles and Techniques

A very comprehensive textbook for a graduate-level course on probabilistic AI.

Location:
Section 7.1, pages 247-251

## See also

- Many computations on multivariate Gaussians are more efficient in information form.
- We saw we can represent multivariate Gaussians in covariance form or information form. These dual representations apply to exponential families more generally.
- Gaussian Markov random fields are a kind of graphical model which captures sparsity in the information form representation.