mlsanityData to 14 Oct 2026

The game theoretic p-Laplacian and semi-supervised learning with few labels

arXiv 1711.10144 ↗First posted 28 Nov 2017math.AP cs.LG cs.NAcited by 22

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Abstract (arXiv)

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.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). First posted on arXiv 28 Nov 2017.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 4; 2023: 4; 2024: 4; 2025: 4; 2026: 3.

22 papers.

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  1. 2021Uniform Convergence Rates for Lipschitz Learning on Graphscited by 9
  2. 2022Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depthcited by 7
  3. 2022Poisson Reweighted Laplacian Uncertainty Sampling for Graph-based Active Learningcited by 6
  4. 2023Graph Laplacian for Semi-Supervised Learningcited by 5
  5. 2021Boundary Estimation from Point Clouds: Algorithms, Guarantees and Applicationscited by 4
  6. 2022Rates of Convergence for Regression with the Graph Poly-Laplaciancited by 4
  7. 2023Transferability of Graph Neural Networks using Graphon and Sampling Theoriescited by 3
  8. 2024Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplaciancited by 3
  9. 2024Numerical solution of a PDE arising from prediction with expert advicecited by 3
  10. 2025Laplace Learning in Wasserstein Spacecited by 3
  11. 2024Improved Graph-based semi-supervised learning Schemescited by 2
  12. 2021Robust Certification for Laplace Learning on Geometric Graphscited by 1
10 more
  1. 2022Learning Label Initialization for Time-Dependent Harmonic Extensioncited by 1
  2. 2024Graph-Based Semi-Supervised Segregated Lipschitz Learningcited by 1
  3. 2025Higher-Order Regularization Learning on Hypergraphscited by 1
  4. 2023Laplacian-based Semi-Supervised Learning in Multilayer Hypergraphs by Coordinate Descentcited by 0
  5. 2023p-Laplacian Transformercited by 0
  6. 2025Convergence of graph Dirichlet energies and graph Laplacians on intersecting manifolds of varying dimensionscited by 0
  7. 2025Energy Approach from varepsilon-Graph to Continuum Diffusion Model with Connectivity Functionalcited by 0
  8. 2026Planner-Admissible Graph-PDE Value Extensions for Sparse Goal-Conditioned Planningcited by 0
  9. 2026A Near-Linear-Time Solver for Graph p-Laplacian Semi-Supervised Learning via Continuation in pcited by 0
  10. 2026Target-Aware State-Adaptive p-Dirichlet Graph Neural Regression for Non-Invasive Body-Composition Estimationcited by 0