  Another facet of the elegant link between random processes on graphs and
Laplacian-based numerical linear algebra is uncovered: based on random spanning
forests, novel Monte-Carlo estimators for graph signal smoothing are proposed.
These random forests are sampled efficiently via a variant of Wilson's
algorithm --in time linear in the number of edges. The theoretical variance of
the proposed estimators are analyzed, and their application to several problems
are considered, such as Tikhonov denoising of graph signals or semi-supervised
learning for node classification on graphs.
