#### Walk-Sum Analysis in Gaussian MRFs

*Jason K. Johnson, Dmitry M. Malioutov, Venkat Chandrasekaran*

An interesting spin-off of Jason's work in GMRFs has been the novel
*walk-sum interpretation* of inference in Gaussian graphical
models. In a technical report, Jason introduced the class of
walk-summable models; characterized some important, easily identified
sub-classes of these models and provided a walk-sum analysis of
certain iterative estimation algorithms, namely, the Gauss-Jacobi
iteration, the (stationary) embedded-tree (ET) algorithm and a
special-case of the cyclic, two-tree ET iteration. Later on, in joint
work with Dmitry Malioutov, this picture was further refined and
applied to give a new interpretation of Gaussian belief propagation,
which was therefore shown to converge in walk-summable models. Later
still, Venkat and Jason generalized the walk-sum interpretation of ET
to a much broader class of algorithms, including iterations based on
arbitrary (non-cyclic) sequences of tractable sub-graphs.