Consistency of semi-supervised learning, stochastic tug-of-war games,
  and the p-Laplacian
Jeff Calder Nadejda Drenska
In this paper we give a broad overview of the intersection of partial
differential equations (PDEs) and graph-based semi-supervised learning. The
overview is focused on a large body of recent work on PDE continuum limits of
graph-based learning, which have been used to prove well-posedness of
semi-supervised learning algorithms in the large data limit. We highlight some
interesting research directions revolving around consistency of graph-based
semi-supervised learning, and present some new results on the consistency of
p-Laplacian semi-supervised learning using the stochastic tug-of-war game
interpretation of the p-Laplacian. We also present the results of some
numerical experiments that illustrate our results and suggest directions for
future work.