information form for multivariate Gaussians
(40 minutes to learn)
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.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ 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
- 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.
- 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