# linear-Gaussian models

## Summary

A linear-Gaussian model is a Bayes net where all the variables are Gaussian, and each variable's mean is linear in the values of its parents. They are widely used because they support efficient inference. Linear dynamical systems are an important special case.

## Context

This concept has the prerequisites:

- multivariate Gaussian distribution (Linear-Gaussian models define multivariate Gaussian distributions.)
- Bayesian networks (Linear-Gaussian models are a kind of Bayes net.)

## 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 7.2, pages 251-254

Additional dependencies:

- information form for multivariate Gaussians

→ Pattern Recognition and Machine Learning

A textbook for a graduate machine learning course, with a focus on Bayesian methods.

Location:
Section 8.1.4, pages 370-371

## See also

- We can answer conditional probability queries using: We can learn the parameters in a linear-Gaussian model using [linear regression](linear_regression) .
- State-space models are an important example of linear-Gaussian models.
- Kalman smoothing can be [viewed](kalman_smoothing_as_bp) " as belief propagation in a linear-Gaussian model.