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

Smoothing graph signals via random spanning forests