The game theoretic p-Laplacian and semi-supervised learning with few labels
This addresses the challenge of learning with limited labeled data in graph-based applications, but appears incremental as it builds on existing p-Laplacian theory.
The paper tackles the problem of semi-supervised learning with few labels on graphs by studying the game theoretic p-Laplacian, showing it is well-posed in the limit of finite labeled and infinite unlabeled data, and proving solutions are approximately Hölder continuous with high probability.
We study the game theoretic p-Laplacian for semi-supervised learning on graphs, and show that it is well-posed in the limit of finite labeled data and infinite unlabeled data. In particular, we show that the continuum limit of graph-based semi-supervised learning with the game theoretic p-Laplacian is a weighted version of the continuous p-Laplace equation. We also prove that solutions to the graph p-Laplace equation are approximately Holder continuous with high probability. Our proof uses the viscosity solution machinery and the maximum principle on a graph.