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.

翻译：本文全面概述了偏微分方程与基于图的半监督学习的交叉领域。我们重点关注近期关于基于图学习的PDE连续极限的大量研究成果，这些成果用于证明半监督学习算法在大数据极限下的适定性。我们围绕基于图半监督学习的一致性提出了若干有趣的研究方向，并利用p-Laplacian的随机拉锯战博弈解释，展示了关于p-Laplacian半监督学习一致性的新结果。同时，我们呈现了一些数值实验的结果，这些实验既验证了我们的结论，也为未来研究指明了潜在方向。