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.