Fundamental Linear Algebra Problem of Gaussian Inference

Understand

Underlying many Bayesian inference techniques that seek to approximate the posterior as a Gaussian distribution is a fundamental linear algebra problem that must be solved for both the mean and key entries of the covariance.

• Even when the true posterior is not Gaussian (e.g., in the case of nonlinear measurement functions) we can use variational schemes that repeatedly solve this linear algebra problem at each iteration.
• In most cases, the question is not whether a solution to this problem exists, but rather how we can exploit problem-specific structure to find it efficiently.
• Our contribution is to clearly state the Fundamental Linear Algebra Problem of Gaussian Inference (FLAPOGI) and to provide a novel presentation (using Kronecker algebra) of the not-so-well-known result of Takahashi et al.