Banded Matrix Operators for Gaussian Markov Models in the Automatic Differentiation Era

These two limitations have been thoroughly Banded matrices can be used as precision studied over the past decades and several approaches matrices in several models including linear have been proposed to overcome them. The most popular state-space models, some Gaussian processes, method for reducing computational complexity is and Gaussian Markov random fields. The the sparse GP framework (Candela and Rasmussen, aim of the paper is to make modern inference 2005; Titsias, 2009), where computations are focussed methods (such as variational inference or on a set of "inducing variables", allowing a tradeoff gradient-based sampling) available for Gaussian between computational requirements and the accuracy models with banded precision.