Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian
It addresses theoretical consistency issues in semi-supervised learning for researchers, but is largely incremental as it builds on existing work.
The paper provides an overview of PDE continuum limits for graph-based semi-supervised learning, focusing on proving well-posedness in the large data limit, and presents new consistency results for p-Laplacian methods using stochastic tug-of-war games, supported by numerical experiments.
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.